解方程:1/(x+1)(x+2)+1/(x+3)(x+4)+……+1/(x+2010)(x+2011)=(2x+4019)/(3x+6033)

解方程:1/(x+1)(x+2)+1/(x+3)(x+4)+……+1/(x+2010)(x+2011)=(2x+4019)/(3x+6033)
其他人气:535 ℃时间:2020-03-27 19:13:36
优质解答
1/(x+1)- 1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)- 1/(x+4)+……+1/(x+2010)- 1/(x+2011)=(2x+4019)/(3x+6033)
1/(x+1)- 1/(x+2011)=(2x+4019)/(3x+6033)
1/(x+1) =(2x+4019)/(3x+6033)+ 1/(x+2011)
1/(x+1) =(2x+4019+3)/[3(x+2011)]
1/(x+1) =[2(x+2011)] /[3(x+2011)]
1/(x+1) =2/3,
X=1/2.
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