Question

一道难度中等的数学题目1/x(x+1)+1/(x+1)(x+2)+……+1/(x+2006)(x+2007)

Answer 1

原式=1/x-1/(1+x)+1/(1+x)-1/(x+2)+……+1/（x+2006)-1/(x+2007)

=1/x-1/(x+2007)=2007/x(x+2007)