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
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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1/2^21/3^2…………………………
1/n^2所以S1^2+ S2^2+S3^2+……Sn^2=
=1+1/2^2+1/3^2+……+1/n^2
=2-1/n