1+ 1/(1+2)+1/(1+2+3)+1/(1+2+3+4）+……+1/(1+2+3+……+100)谢谢
问题描述：
1+ 1/(1+2)+1/(1+2+3)+1/(1+2+3+4）+……+1/(1+2+3+……+100)谢谢
答
1+2+……+n=n(n+1)/2所以1/(1+2+……+n)=2/n(n+1)=2*[1/n-1/(n+1)]所以1/(1+2)=2*(1/2-1/3)……1/(1+2+……+100)=2*(1/100-1/101)而1=2*(1-1/2)所以1+1/(1+2)+1/(1+2+3)+(1/1+2+3+4)+...+1/(1+2+3+...+100)=2*[(1-1/...