计算这个式子:1/a(a+1)+1/(a+1)(a+2)+.+1/(a+9)(a+10)

问题描述:

计算这个式子:1/a(a+1)+1/(a+1)(a+2)+.+1/(a+9)(a+10)

1/a-1/(a+1)+1/(a+1)-1/(a+2)+......-1/(a+10)=1/a-1/(a+10)

裂项相消
原式=1/a-1/(a+1)+1/(a+1)-1/(a+2)+...+1/(a+10)
=1/a-1/(a+10)