1/(x+1)(x+2)+1/(x+2)(x+3)+…+1/(x+99)(x+100)

世上第一丑男2022-10-04 11:39:541条回答

已提交,审核后显示!提交回复

共1条回复
娟娟925 共回答了16个问题 | 采纳率93.8%
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+99)(x+100)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+99)-1/(x+100)
=1/x-1/(x+100)
=100/[x(x+100)]
1年前

相关推荐

1/(X+1)(X+2)+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)=1/2X+4012
旋转的木马991年前3
轮日 共回答了16个问题 | 采纳率87.5%
1/(X+1)(X+2)+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)=1/2X+4012
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+2005)-1/(x+2006)=1/2(x+2006)
1/(x+1)-1/(x+2006)=(1/2)*1/(x+2006)
1/(x+1)=(3/2)*1/(x+2006)
3(x+1)=2(x+2006)
x=4012-3
x=4009
解方程:1/x(x+2)+1/(x+1)(x+3)+…+1/(x+8)(x+10)=0
众网友1年前2
yiguo765 共回答了15个问题 | 采纳率100%
1/2*[1/x-1/(x+2)]+1/2*[1/(x+1)-1/(x+3)]+…+1/2*[1/(x+8)-1/(x+10)]=0
1/2*[1/x-1/(x+2)+1/(x+1)-1/(x+3)+1/(x+2)-1/(x+4)+…+1/(x+8)-1/(x+10)]=0
1/2*[1/x+1/(x+1)-1/(x+9)-1/(x+10)]=0
所以1/x+1/(x+1)-1/(x+9)-1/(x+10)=0
[1/x-1/(x+9)]+[1/(x+1)-1/(x+10)]=0
9/[x(x+9)]+9/[(x+1)(x+10)]=0
9/[x(x+9)]=-9/[(x+1)(x+10)]
所以x(x+9)=-(x+1)(x+10)
x^2+9x=-(x^2+11x+10)
x^2+9x+x^2+11x+10=0
2x^2+20x+10=0
x^2+10x+5=0
x=-5±2√5
打字不易,
1/(X+2)+1/(X+5)=1/(X+3)+1/(X+4)江湖救急,方程求解!
一剑红飘1年前3
leonzhang 共回答了15个问题 | 采纳率80%
1/(X+2)+1/(X+5)=1/(X+3)+1/(X+4)移项
1/(X+2)-1/(X+3)=1/(X+4)-1/(X+5)
左右分别通分得(X+2)(X+3)=(X+4)(X+5)
展开后得4x=-14 所以x=-7/2
(X²-X-5)/X+2=(X+2)+1/(X+2)-5是如何化简的来的,
(X²-X-5)/X+2=(X+2)+1/(X+2)-5是如何化简的来的,
moneyowner1年前2
kagensea 共回答了20个问题 | 采纳率70%
(X²-X-5)/(X+2)
=[(x^2+4x+4)-(5x+10)+1]/(x+2)
=[(x+2)^2-5(x+2)+1]/(x+2)
=(x+2)+1/(x+2)-5