By considering $\mathrm{f}\left( r \right)-\mathrm{f}\left( r+1 \right)$, where $\mathrm{f}\left( r

Question

By considering $\mathrm{f}\left( r \right)-\mathrm{f}\left( r+1 \right)$, where $\mathrm{f}\left( r \right)=\frac{1}{r}$, find the sum to $2n$ terms of the series $\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...$ Show that the sum to $2n$ terms of the series $\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}}+\frac{1}{{{4}^{2}}}+\frac{1}{{{5}^{2}}}+...$ is less than $1$.

Accepted Answer

(i) $1-\frac1{2n+1}$; (ii) $\frac1{2^2}+\frac1{3^2}+\frac1{4^2}+\cdots<1$

Application of Sum to Infinity Q3

Application of Sum to Infinity Q3

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