Question

已知数列{an}的前n项和为Sn,且满足a1=1,an+SnSn-1=0 an=1/n(1-n),Sn=1/n

Answer 1

已知数列{an}的前n项和为Sn,且满足a1=1,an+SnSn-1=0 an=1/n(1-n), Sn=1/n

求证:S1^2+ S2^2+S3^2+……Sn^2 ≤2-1/n

因Sn=1/n,所以

S1^2+ S2^2+S3^2+……Sn^2=

=1+1/2^2+1/3^2+……+1/n^2

因为

1/2^2