Question

- -.这道题为啥选第一个.

Answer 1

1+2+3+...+n=n(n+1)/2

an=2/[n(n+1)]

sn=a1+a2+a3+...+an=2/(1*2)+2/(2*3)+...+2/[n(n+1)]

=2{1/(1*2)+1/(2*3)+1/(3*4)+...+1/[n(n+1)]}

=2{(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+[1/n-1/(n+1)]}

=2[1-1/(n+1)]

=2*n/(n+1)

所以选（1）