1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+```+1/(1+2+3+```+100)＝?
问题描述：
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+```+1/(1+2+3+```+100)＝?
答
1/(1+2+...+n)=2/[n(n+1)]=2/n-2/(n+1)
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+```+1/(1+2+3+```+100)
=2/1-2/2+2/2-2/3+2/3-2/4+.+2/100-2/101
=2-2/101=200/101