数列an是首项为3公差为2的等差数列其前n项和为Sn求An=1/S1+1/S2+1/S3+...+1/Sn

题目

数列an是首项为3公差为2的等差数列其前n项和为Sn求An=1/S1+1/S2+1/S3+...+1/Sn

答案

an = a1 + (n-1)d = 2n + 1
Sn = [n(a1 + an)]/2 = n(n+2)
1/Sn = 1/n(n+2) = [1/n - 1/(n+2)]/2
An = S1 + S2+ ...+ Sn = 21/40 - (2n+3)/2(n+2)(n+1)