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Question Number 147737 by liberty last updated on 23/Jul/21

Σ_(n≥1) (1/n^2 )(1+(1/2)+(1/3)+...+(1/n))^2 =?

∑n⩾11n2(1+12+13+...+1n)2=?

Answered by ArielVyny last updated on 24/Jul/21

(Σ_(n≥1) (1/n))^2 ≤Σ(1/n^2 )=(π^2 /6) (Σ_(n≥1) (1/n))^2 Σ_(n≥1) (1/n^2 )≤(π^4 /(36))

(∑n⩾11n)2⩽Σ1n2=π26(∑n⩾11n)2∑n⩾11n2⩽π436

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