1/(1x3)+1/(3x5)+1/(5x7)+.+1/2005x2007=?

娥魅2022-10-04 11:39:545条回答

1/(1x3)+1/(3x5)+1/(5x7)+.+1/2005x2007=?
例子：2/(1X3)=1-(1/3)
2/(3X5)=(1/3)-(1/5)
2/(5X7)=(1/5)-(1/7)

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xty91575 共回答了13个问题 | 采纳率84.6%: 1/(1x3)+1/(3x5)+1/(5x7)+.+1/2005x2007
=（1-1/3+1/3-1/5+1/5-1/7+……+1/2005-1/2007）÷2
=（1-1/2007）÷2
=2006/2007÷2
=1003/2007; 1年前

fanfan 共回答了20个问题 | 采纳率: 这个问题用裂项相消法求解.1/(1X3)=1/2[1-(1/3)],1/(3X5)=1/2[(1/3)-(1/5)],
1/(5X7)=1/2[(1/5)-(1/7)],.......,1/2005x2007=1/2[1/2005-1/2007].所以
1/(1x3)+1/(3x5)+1/(5x7)+.......+1/2005x2007=1/2(1-1/3+1/3-1/5+1/5-1/7+.........+1/2005-1/2007)
=1/2(1-1/2007); 1年前

nccmx2000 共回答了6个问题 | 采纳率: =[2/(1x3)+2/(3x5)+2/(5x7)+.......+2/2005x2007]/2
=[1-(1/3)+(1/3)-(1/5).......+1/2005-1/2007]/2
=(1-1/2007)/2
=1003/2007; 1年前

司马欣共回答了3个问题 | 采纳率: 貌似楼主已有答案啊
1/2*(1-1/3+1/3-1/5+1/5-1/7.....+1/2005-1/2007)
=1/2*(1-1/2007)
=1003/2007; 1年前

用数学归纳法证明1/(1x3)+1/(3x5)+1/(5x7)…1/(2n-1)(2n+1)=n/(2n+1) 用数学归纳法证明1/(1x3)+1/(3x5)+1/(5x7)…1/(2n-1)(2n+1)=n/(2n+1) 我证明完n=k+1后与结论不符,不知哪错了 当n=k时成立 即1/(1x3)+1/(3x5)+1/(5x7)…1/(2k-1)(2k+1)=k/(2k+1) 则n=k+1时 1/(1x3)+1/(3x5)+1/(5x7)…1/(2k-1)(2k+1)+1/(2k+1)(2k+3) =k/(2k+1)+1/(2k+1)(2k+3) =2k^2+3k+1/(2k+1)(2k+3) =(k+1/2)(k+1)/(2k+1)(2k+3) =(k+1)/2(2k+3) 而原式应为(k+1)/(2k+3) zl88081年前1: a江心a 共回答了25个问题 | 采纳率96%

=k/(2k+1)+1/(2k+1)(2k+3)
=（2k+1）（k+1/（2k+3））
=（2k+1）（(2k方+3k+1)/（2k+3））
=1/（2k+1）*（(2k+1)（k+1）/（2k+3））
=（k+1）/（2k+3）成立
你算的
=(2k^2+3k+1）/(2k+1)(2k+3)
=（2k+1）（k+1）/(2k+1)(2k+3)
=（k+1）/（2k+3）
哪来的1/2

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1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11).1/(97x99)=多少?这个肯定得用 1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11).1/(97x99)=多少?这个肯定得用简便方法,请指教. ww120106kk1年前1: caihuameimei 共回答了22个问题 | 采纳率81.8%

您好
1/(1x3) = (1-1/3)/2
那么1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11).1/(97x99)
=（1-1/3)/2+（1/3-1/5)/2+(1/5-1/7)/2+.+(1/97-1/99)/2
=(1-1/3+1/3-1/5+1/5-1/7+.-1/97+1/97-1/99)/2
=(1-1/99)X2
=49/99

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1/(1x3)+1/(3x5)+1/(5x7)+.+1/2005x2007=? 1/(1x3)+1/(3x5)+1/(5x7)+.+1/2005x2007=? 例子：2/(1X3)=1-(1/3) 2/(3X5)=(1/3)-(1/5) 2/(5X7)=(1/5)-(1/7) 落英无痕361年前6: 贴完所有mm 共回答了15个问题 | 采纳率93.3%

你好：
1/(1x3)+1/(3x5)+1/(5x7)+.+1/2005x2007
=1/2×（1-1/3+1/3-1/5+1/5-1/7+.+1/2005-1/2007）
=1/2×（1-1/2007）
=1/2×2006/2007
=1003/2007

1年前查看全部