Question

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

Answer 1

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.