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Question Number 147670 by mnjuly1970 last updated on 22/Jul/21

Answered by Olaf_Thorendsen last updated on 22/Jul/21

$$\mathrm{By}\mathrm{definition}{\mathrm{H}}_n^{\left(2\right)}=\underset{k=1}{\sum ^n}\frac{1}{k^2}$$$$\Rightarrow {\mathrm{H}}_{n-1}^{\left(2\right)}+\frac{1}{n^2}=\underset{k=1}{\sum ^{n-1}}\frac{1}{k^2}+\frac{1}{n^2}={\mathrm{H}}_n^{\left(2\right)}$$$$\mathrm{Trivial}.$$

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