Question

设数列{an}前n项和为Sn,已知(1/S1)+(1/S2)+....+(1/Sn)=n/(n+1),求S1,S2及Sn

急

Answer 1

用[(1/S1)+(1/S2)+....+(1/Sn)=n/(n+1)]-[(1/S1)+(1/S2)+....+(1/Sn-1)=n-1/n]
可得1/Sn=(n-1)/n+n/(n+1)，进而可求S1、S2、Sn.