用Limit Comparison Test判断级数的收敛和发散

罗小白2022-10-04 11:39:541条回答

用Limit Comparison Test判断级数的收敛和发散
∑(n从1到正无穷)(5n+2)/(3n^3+2N^2+n+1)

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q741963 共回答了18个问题 | 采纳率88.9%
是这样的,找一个合适的candidate
怎么找呢,一般是让n趋于无穷,然后看leading order
n->无穷
5n+2~5n,因为n很大,2相比之下非常的小
3n^3+2N^2+n+1~3n^3, 同样的道理
所以我们的candidate出现了就是
bn=5n/3n^3=5/(3n^2)
an=(5n+2)/(3n^3+2N^2+n+1)
因为无法直接判断an,bn的大小关系,所以一般的Comparison Test不适用
所以利用Limit Comparison Test
lim n->无穷 an/bn
=[(5n+2)/(3n^3+2N^2+n+1)]*[3n^2/5]
=(15n^3+6n^2)/5(3n^3+2N^2+n+1)
上下同除n^3
=(15+6/n)/5(3+2/n+1/n^2+1/n^3)
当n趋向无穷时,1/n,1/n^2,1/n^3->0
所以
lim n->无穷 an/bn=(15+0)/3*(5+0+0+0)=1>0
由Limit Comparison Test
只要极限是一个大于0,有限的常数,则Σan和Σbn同时发散或者同时收敛
对于Σbn=(5/3)Σ1/n^2
由p-test, p=2>1,所以Σbn收敛
所以原级数∑(n从1到正无穷)(5n+2)/(3n^3+2N^2+n+1)收敛
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considered to be made of single molecular layers that lie flat
on the surface (Figure S1 in the Supporting Information).The
4-nm high fibers are made of two such piled up layers,with
their alkyl chains still lying parallel to the surface.
w3281年前1
熊猫烧香SSS 共回答了19个问题 | 采纳率84.2%
沿着柱体轴线的堆积周期性和沿着分子盘法线(molecular disc normal)的堆积周期性(分别为h0和h)表明,分子几乎垂直于柱体轴线而堆积(参见支持信息中的表S1)[16].而且,为了填满邻近分子之间可得的空间,分子很可能以交替的形式堆积.这也被分子动力学(MD)仿真所表明,在此仿真中,遵照实验的X射线数据,由一个高度为13.3-Å(4×3.33 Å相当于4个堆积分子)的周期性的圆柱细胞建立了一个柱体模型.这些计算表明,可得的体积有良好的空间填充,以及在整个仿真实验时间内微偏析的增强,从而对柱状结构的内聚性做出了贡献.而且,该模型表明,柱体的内聚由于Pt-Pt和Pt-炔烃的互作用而进一步得到增强,就如也被尖锐的宽角度信号(h0)所揭示的那样.BF4-阴离子位于络合物之间.MD实验的快照解释了2c在六边形柱体(Colh)相中优异的分子包装,如图4所示的那样.
中心的刚性富电子核心的大小大约为2nm,这是一个非常接近于如2b在稀释凝胶下用TEM确定的一根纤维的最小宽度的值.
最后还研究了在定义良好的结晶学表面(例如云母和高度有序的热解石墨(HOPG)上的这些纤丝状超结构的组织(注意,分子沉积在无定形碳薄膜上用于TEM研究).2b的稀释凝胶(0.08m mol L-1)用滴铸(drop casting)法沉积在云母基体上.如图5a中所示的那样,没有表观取向次序和平均高度为2nm的纤维清晰可见(参见图5b的横截面)
令人感兴趣的是,用旋转涂覆沉积在新鲜劈开的HOPG上的化合物2b的稀释的十二烷凝胶导致了分子纤维的自组合,它主要遵循着下面HOPG基体的优先结晶学方向(图5c).片段图形三倍的对称性在纤维相互形成60°和120°角度的截距处特别可以看出.这些横截面表明了存在两种纤维,它们相应于两种不同的分子高度,即(2.0±0.1)nm和(4.0±0.3nm)(图5d).此2nm高的纤维可以认为是由平坦处于表面上的单一的分子层构成的(支持信息中的图S1).4nm高的纤维由两层这样堆积起来的层构成,它们的烷烃链仍与表面处于平行.
I think there's no comparison between the two cars,one __cle
I think there's no comparison between the two cars,one __clearly far better than the other.
A,being B,was C,having been D,be 答案上写什么考察独立主格,我百度了独立主格,看的灰常迷惑啊.为什么要选A.本人初学英语,头脑有限,望各位不要讲解的太高深.
Z00001年前2
ni75560 共回答了16个问题 | 采纳率81.3%
很简单,你看前半句已经具有主谓宾了,是个完整句子.后半句又不是引导出来的从句,所以肯定不能再用谓语动词了.主句时态是现在时,所以用BEING.
大家能帮看看我的语法有错误吗?we can make a comparison from the two picture
大家能帮看看我的语法有错误吗?
we can make a comparison from the two pictures.the whole structure,including it's wing and tail even its head were imitated the bird.我想表达的意思是,从这两张图片的对比中我们可以发现,飞机的整个结构,包括飞机的翅膀,尾翼,头部都是在模仿鸟儿.我一直觉得最后一句的were imitated有点问题,我在这想用一个一般过去时,我是不是应该要把were去掉,还是说把were换成are?怎么用比较好?或者说句子是对的?
chiefind1年前1
文幻绮影 共回答了11个问题 | 采纳率90.9%
是的,把were换成are.
英语IQ题1.which ONE OF THE FIVE MAKES THE BEST COMPARISON?TREE
英语IQ题
1.which ONE OF THE FIVE MAKES THE BEST COMPARISON?TREE IS TO GROUND AS CHIMNEY IS TO :SMOKE BRICK SKY GARAGE HOUSE 2.WHICH ONE OF THE FIVE IS LEAST LIKE THE OTHER FOUR?TOUCH TASTE HEAR SMILE SEE 3.WHICH ONE OF THE FIVE IS LEAST LIKE THE OTHER FOUR:POTATO CORN APPLE CARROT BEAN
朗中江湖1年前1
Jason_D 共回答了25个问题 | 采纳率100%
house smile apple
A metaphor is a poetic device that deals with comparison. It
A metaphor is a poetic device that deals with comparison. It compares similar qualities of two dissimilar objects. With a simple metaphor, one object becomes the other: Love is a rose. Although this does not sound like a particularly rich image, a metaphor can communicate so much about a particular image that poets use them more than any other type of figurative language(修辞). The reason for this is that poets compose their poetry to express what they are experiencing emotionally at that moment. Consequently, what the poet imagines love to be may or may not be love we see it. Therefore, the poet’s job is to enable us to experience it, to feel it the same way as the poet does.
Let’s analyze this remarkably unsophisticated metaphor concerning love and the rose to see what it offers. Because the poet uses a comparison with a rose, first we must examine the characteristics of that flower. A rose is spectacular in its beauty; its petals(花瓣) are nicely soft, and its smell is pleasing. It’s possible to say that a rose is actually a feast to the senses of sight, touch, and smell. The rose’s appearance seems to border on(近似于)perfection, each petal seemingly symmetrical(对称的) in form. Isn’t this the way one’s love should be? A loved one should be a delight to one’s senses and seem perfect. However, there is another dimension added to the comparison by using a rose. Roses have thorns(刺). The poet wants to convey the idea that roses can be tricky(机警的). So can love, the metaphor tells us. When one reaches out with absolute trust to touch the object of his or her affection, ouch, a thorn can cause great harm! “Be careful,” the metaphor warns: Love is a feast to the senses, but it can overwhelm us, and it can also hurt us and cause acute suffering. This is the poet’s perception of love--a warning. What is the point? Just this: It took almost 14 sentences to clarify what a simple metaphor communicates in only four words! That is the artistry and the joy of the simple metaphor.
小题1:According to the passage, what is a metaphor?
A.A comparison between two different objects with similar features.
B.A contrast between two different things to create a vivid image.
C.A description of two similar objects in a poetic way.
D.A literary device specially employed in poetry writing.
小题2: The main idea of this passage is that .
A.rose is a good image in poetry B.love is sweet and pleasing
C.metaphor is ambiguous D.metaphor is great poetic device
小题3: It can be inferred from the passage that a metaphor is .
A.difficult to understand B.rich in meaning C.not precise enough D.like a flower
小题4: As is meant by the author, thorns of a rose_________.
A.protect the rose from harm B.symbolize reduced love
C.add a new element to the image of love D.represent objects of one’s affection
小题5: The meaning of the love-is–a-rose metaphor is that____________-
A.love is a true joy B.true love comes once in a lifetime
C.love does not last long D.love is both good and bad experiences
郑重1年前1
txin 共回答了16个问题 | 采纳率93.8%
小题1:A小题1:D小题1:B小题1:C小题1:D

examining differences,making comparisonsm,是什么意思?
兜兜梨327号1年前1
wdccwdcc 共回答了20个问题 | 采纳率85%
检查差异 进行比较
英语翻译XXandXXnoted that in comparison to physical stores,when
英语翻译
XXandXXnoted that in comparison to physical stores,when shopping on the internet,there were no store lines or unhelpful staff,travelling in bad weather,nor any transport costs involved.
刚毕业的孩子1年前8
lfgfaw 共回答了18个问题 | 采纳率94.4%
XX和XX表明,相对于现实中的商店,网购无需排队,也没有毫无帮助的店员,还避免了在坏天气里出行的烦恼,同时节省了那些交通费.
rod在物理中的意义an object with one dimension small in comparison w
rod在物理中的意义
an object with one dimension small in comparison with another(such as a metre or a beam) can be modelled as rod.This means that the mass of the object can be considerdto be distributed along a straight line,A rod has no thickness(it is one-dimensional) and is rigid(it does not bend or buckle)
上面是解释,rod是“刚体”吗?能否大概解释一下这段话的意思~
seek_better1年前0
共回答了个问题 | 采纳率
请问make a comparison 和 pose a contrast的区别在哪里?
hannahyang1年前1
0f7ezm1 共回答了15个问题 | 采纳率86.7%
comparison 可以有相同的也可以由不同的.
pose a contrast特指不同的地方~
comparison "a rose for emily" by William Faulkner and "the l
comparison "a rose for emily" by William Faulkner and "the loons"by Margaret Laurence
I need a essay of a comparison between "ä rose for emily"and "the loons" in topic of symbolize or setting of use in those two article.
忘情y1年前1
liguowei0 共回答了21个问题 | 采纳率95.2%
"A Rose for Emily" evokes the terms Southern gothic and grotesque,two types of literature in which the general tone is one of gloom,terror,and understated violence.The story is Faulkner’s best example of these forms because it contains unimaginably dark images; And show out the nouthen nobility's downfallen and decayed history,all the book is full in grotesque and gothic.
"The Loons" show out the one tragic fate of an Indian,used high artistic expression,fresh and pretty language,the true feelings description to show out the Indian that lived in social edge.The tragic ends make many readers sympathy.
英语翻译The performance advantage of Reviser in comparison toful
英语翻译
The performance advantage of Reviser in comparison to
full recomputations is visible best when applied repeatedly.
When we assume that the static analysis is performed on a
continuous-integration server for every check-in into a version
control system,savings are accumulated over time as depicted
on the right sides of Figures 5{11.For instance,over the 25
most recent Soot revisions,the 75% savings introduced by
Reviser accumulate to over 11,000 seconds (3 hours).
In general,the performance of Reviser depends on the
number of jump functions that need to be recomputed.The
larger the impact of the code change is,the more edges are
ax0bected.Clearing and repropagating over an edge takes
generally longer than the initial computation for that edge.
Performance gains are thus achieved by recomputing only (a
sux0eciently precise overapproximation of) the ax0bected nodes
which is usually a small subset of all nodes in the program
graph.In the worst case,all edges must be recomputed and
the algorithm degenerates to a recomputation with some
overhead,caused by changeset computation and wrapper
lookups as described in Section 4.This,for instance,happens
for the JUnit update from version 4.10 to version 4.11.
melodyyun1年前1
discover1981 共回答了18个问题 | 采纳率88.9%
相比校订者的性能优势
全部重新计算可见最好反复应用.
当我们假定在一个执行静态分析
持续集成服务器每签入到版本
控制系统、储蓄积累随着时间的描述
右边的图5 { 11.例如,在25岁
最近的烟灰修订,75%的储蓄了
校订者积累超过11000秒(3个小时).
一般来说,校订者取决于的性能
跳数的函数需要重新计算.的
更大的代码变化的影响,更多的边缘
aected.清算和repropagating优势需要
一般超过最初的计算优势.
性能因此只通过验算(
suciently精确overapproximation aected节点
这是通常的一个小子集中的所有节点计划
图.在最坏的情况下,所有的边缘必须重新计算
重新计算一些算法退化
开销,由于变更集计算和包装
查找如第四节所述.例如,这发生
对于JUnit更新从4.10版到4.11版.
Comparison with state-of-the-art methods
tianzhike1年前3
小小祭祀 共回答了18个问题 | 采纳率94.4%
“用最新的/先进的方法对比分析”
其中state-of-the-art意思是“(尤其指科学技术)最新的,最尖端的,最先进的”
谁能帮我找下这篇论文Li Jingwen.A comparison of Chinese and U.S.product
谁能帮我找下这篇论文Li Jingwen.A comparison of Chinese and U.S.productivity
Li Jingwen.A comparison of Chinese and U.S.productivity:Sino-American economic and trade relations[J].Journal of Asian Economics,1994,5(1):85-97.百度上能找到 但是要钱.
僵硬的棉被1年前1
_阿兵_ 共回答了16个问题 | 采纳率100%
哈……我可以下得到论文……但翻译是有偿的啊……一共13页的论文,至少要500块钱啊……
There's no comparison between them,one being clearly much be
There's no comparison between them,one being clearly much better than the other为啥是being?
兔子不吃窝边草1年前2
xuflyan 共回答了20个问题 | 采纳率90%
这个句子是非谓语哦·
分解成俩个句子就是:
There's no comparison between them 他们俩个没有可比性
One is clearly much better than the other 一个明显优于另外一个.
俩个句子放在一起,又没有连接词,只能用非谓语了····being后边是个独立主格结构,在句中作状语,主语不是个句子
【俊狼猎英】 欢迎追问
I think there's nocomparison between the two cars ,on ___cle
I think there's nocomparison between the two cars ,on ___clearly far better than the other.
A.being B.was C.having been D.be
冷无言就是我1年前1
木石山水 共回答了20个问题 | 采纳率95%
I think there's nocomparison between the two cars,ONE (我觉得应该是ONE) being clearly far better than the other.
one being clearly far better than the other
是现在分词短语表示伴随情况.
意思是:
一辆比另一辆明显好那么多,我认为两辆车根本不用比.
No man is happy but comparison .
沃熙1年前3
feierle 共回答了16个问题 | 采纳率81.3%
有比较才有快乐.这里的comparison是比较的意思,but是除了.的意思,也就是说这句话直译可以说成“如果不比较,那么没有人是快乐的”.不错的句子哈
1.A comparison of your offer our regular suppliers shows tha
1.A comparison of your offer our regular suppliers shows that their figures are more favorable.
A.with that of B.with what of C.with which of D.with this of
2.If your prices are competitive,we are confident the goods in great quantities in this market.
A.to sell B.to be selling C.in being sold D.in selling
3.We confirm our fax just sent these goods.
A.offering you firm B.firm offering you
C.to be offered to you firm D.to firm offer you
4.We offer you the following items your reply reaching here by 4 p.m.Today our time .
A.subjecting to B.to subject to C.subjects to D.subject to
5.Although we appreciate good quality of your goods,we are sorry to say that your prices appear to be .
A.of the high standard B.in the high level
C.on the high side D.at the high end
6.We trust that we may be with a continuance of your valued orders.
A.favor B.favoring C.favored D.do a favor
7.We hope that you will see your way to us your order,and assure you in advance of its most careful execution.
A.supply B.grant C.leave D.place
8.Not having heard from you since,we should be glad to know whether there is any disadvantages in our terms which we could .
A.engage B.remove C.give D.move
9.You are that we will quote our best prices as soon as we are told what products of ours you need.
A.sure B.ensured C.assured D.entrusted
10.In all probability this offer will not be for some time,and we according look forward to receiving an early reply from you.
A.repeated B.made C.given D.supplied
ccz55661年前2
yjq510 共回答了21个问题 | 采纳率85.7%
1,A.2,D.confident of/in 有信心 .3,D,We confirm our fax just sent// (to firm offer you these goods)目的.4,D,subject 是adj,be subject to根据…….5,B,in the high lever ,形容的是价格.6,C,(favor 的过去...
英语中形容词的用法看一篇文章,里面写“By comparison my family, the Santos, are
英语中形容词的用法
看一篇文章,里面写“By comparison my family, the Santos, are traveling light through time."
后面题目答案说这里”light“是形容词”unencumbered“的意思,但是按理说形容词是不能修饰travel动词的.
不知道是不是因为这里用的现在进行时的原因,还是美国人写东西不拘小节,但是这可是SAT的文章啊啊!
y5566991年前2
南雁vs北牧 共回答了23个问题 | 采纳率91.3%
形容词可以作伴随状语
如:i went home ,tired and exhausted
当然也有人认为是主语补足语
are traveling light 中light 是形容词作伴随状语
A Comparison between the Spring Festival and Christmas
A Comparison between the Spring Festival and Christmas
用英语介绍两个节日的不同之处和相同之处!
仙奇侠1年前4
阿冥 共回答了15个问题 | 采纳率86.7%
The Sping Festival and Christmas have much in common.Both are prepared beforehand to create a joyous atmosphere;both offer a family reunion with asquare feast;and both satisfy the childeen with new clothes,loverly presents and delicious food.However,the
Chinese Spring festival has no religious backgroind while Christmas has something to do with God and there is Santa Claus with white beard to bring children presents.The westerners send each other Christmas cards for greetings while the Chinese people pay a call on each other.
The Spring Festival is the most important festival for the Chinese people and is when all family members get together,just like Christmas in the West.All people living away from home go back,becoming the busiest time for transportation systems of about half a month from the Spring Festival.Airports,railway stations and long-distance bus stations are crowded with home returnees.
Strictly speaking,the Spring Festival starts every year in the early days of the 12th lunar month and will last till the mid 1st lunar month of the next year.Of them,the most important days are Spring Festival Eve and the first three days.The Chinese government now stipulates people have seven days off for the Chinese Lunar New Year.
Christmas Day,the 25th of December,is the biggest festival celebrated in the Christian countries of the world.Christmas regard this day as the birthday of Jesus Christ,but many of the customs and celebrations are not of a religious1 nature.
In the large shops preparations for Christmas are begun five or six weeks before the actual day.Shop owners like Christmas because it is a time when people exchange2 presents.This means more goods are bought than at any other time of the year.In larger towns decorations3 are put up in the main street two or three weeks before Christmas---usually these decorations are lit up at night.
Preparations are also made at home.Special puddings and cakes are eaten on Christmas Day and these have to be made three or four weeks in advance4.Two or three days before Christmas,people decorate their houses with paper decorations and leaves and branches.People also like to have a Christmas tree in the living room.This is a very small fir tree decorated with silver paper and colored lights.
nowadays,some of the Chinese youth has begun to celebeate Christmas,following the example of the westerners.Perhaps they do so just for fun and out of curiosity.
VC++6.0下Warning:comparison between pointer and integer Error
VC++6.0下Warning:comparison between pointer and integer Error:too few arguments to function ‘feof
这个警告和错误一般来说是什么意思.如何解决,大体说一下.
waterstoneyy1年前1
xuzhisheng43 共回答了18个问题 | 采纳率88.9%
说明你调用函数feof时参数有问题,参数个数或类型
1.和市区比较起来,这个地方相当安静(comparison,rather)
1.和市区比较起来,这个地方相当安静(comparison,rather)
2.据说莎士比亚曾把他爱的那个女士比喻为夏天(shakespeare,compare)
3.我打算向他们的经理抱怨外面的噪声(intend,complaint)
4.向***隐藏证据是严重的罪行(conceal,serious)
5.他们有完全成功的把握,但却被告诉比赛取消了(confidence,only,inform,cancel)
青青草果1年前1
小鸟888 共回答了19个问题 | 采纳率89.5%
1.By comparison with the urban district,this place is rather quiet.
2.It is said that Shakespeare had compared the lady he loved as the summer.
3.I intend to complaint to their manager about the noice outside.
4.Concealing evidences from the police is a serious crime.
5.They were of great confidence that they would win,only informed that the match was cancelled.
in comparison to 和 compared with 有什么区别?
yzms1年前1
女吉诃德 共回答了29个问题 | 采纳率93.1%
in comparison to ---- prep.相较,同...比较起来
compared with --- vbl.和...相比;与...比较起来
如:Walking can't compare with flying.
走路比不上飞行.
perform a comparison with carriers’ data where required的wher
perform a comparison with carriers’ data where required的where是甚麼意思
这里的where是甚麼样的用法?感觉不是那里的意思
magician9823301年前1
kingwav 共回答了19个问题 | 采纳率94.7%
where是关系副词,表示地方
where required 在必要的地方
类似的副词还有when,when required 在必要的时候
整句翻译:
在必要的地方跟carrier的数据进行比较
这里carrier我没有给出固定翻译,因为它有很多意思,你可以根据这个句子的上下文来选一个合适的意思:
电话运营商/货运公司/货运人/班机/媒介/航空母舰
in comparison to 和 compared with 有什么区别?
落落之华1年前1
摩登0666 共回答了24个问题 | 采纳率83.3%
in comparison to ---- prep.相较,同...比较起来x0dcompared with --- vbl.和...相比;与...比较起来x0d如:Walking can't compare with flying.x0d走路比不上飞行.
求英语高手:make a comparison和pose a contrast的区别
求英语高手:make a comparison和pose a contrast的区别
经常在做英语阅读阅读练习的时候碰到.
FANNG1年前1
sosvs 共回答了15个问题 | 采纳率80%
comparison是类比,即比较共同点,也就是相差不大;contrast是对比,即比较差异,差距很大.
英语翻译Generation Cohorts and Personal Values:A Comparison of C
英语翻译
Generation Cohorts and Personal Values:A Comparison of China and the U.S.这个句子里的Generation Cohort 怎么翻译好呢,
兰草席1年前1
zjwlw007 共回答了23个问题 | 采纳率82.6%
代队列
英语用词的正确形式填空If you ______(comparison) these two articles,you
英语用词的正确形式填空
If you ______(comparison) these two articles,you will find they have the same opinion.
小生82291年前2
yewenjun00 共回答了18个问题 | 采纳率88.9%
compare,用动词原形
where 的其他用法perform a comparison with carriers’ data where re
where 的其他用法
perform a comparison with carriers’ data where required
这里的where甚麼意思啊?那是一种甚麼用法呢
lolay511年前1
上衣口袋_ 共回答了16个问题 | 采纳率81.3%
where的意思是在哪里,到哪里.一般都是用在问句的开头,提问在哪里或到哪里是就是采用where.
一个英语句子,帮着看一下,谢谢 首先,句子是a comparison of British geological pub
一个英语句子,帮着看一下,谢谢 首先,句子是a comparison of British geological publications over th
一个英语句子,帮着看一下,谢谢
首先,句子是a comparison of British geological publications over the last century and a half reveals not simply an increasing emphasis on the primacy of research, but also a changing definition of what constitutes an acceptable research paper.
问题是,1,这句话怎么翻译通顺呢?,2,the last century and a half reveals not 这一词组中,half 是与前面组合成 上一个半世纪呢,还是与后面组合成 一半的(出版物) 呢?
谢谢!
cancers1年前4
chippe 共回答了19个问题 | 采纳率78.9%
问题1,a comparison of British geological publications over the last century and a half对于过去一个半世纪的英国地质学领域的出版物的比较,reveals not simply an increasing emphasis on the primacy of research其揭示了不仅是越来越强调科研的主导地位,but also a changing definition of what constitutes an acceptable research paper.也在于可接受的科研论文组成的定义的改变.问题2,句子的主语其实是a comparson(单数),所以 reveal加了s,如果说是指一半的出版物(a half of the publications)里面就不止2个了,是复数,那么reveal 就不需要加s.所以这里的half 是与前者相连,是指 the last century and a half,过去一个半世纪.希望我这样的解释对你有所帮助.晚安.