等差数列{an}=2n+1,前n项和为Sn,求1/S1+1/S2+.+1/Sn
问题描述：
等差数列{an}=2n+1,前n项和为Sn,求1/S1+1/S2+.+1/Sn
答
an=2n+1Sn=n(a1+an)/2=n(3+2n+1)/2=n(n+2)所以1/Sn=1/n(n+2)=[1/n-1/(n+2)]/2那么1/S1+1/S2+.+1/Sn=(1-1/3)/2+(1/2-1/4)/2+(1/3-1/5)/2+...+[1/n-1/(n+2)]/2=[1+1/2-1/(n+1)-1/(n+2)]/2=3/4-(2n+3)/2(n+1)(n+2)如果...