Application of Sum to Infinity Q3
(i)
(i) By considering $\text{f}\left( r \right)-\text{f}\left( r+1 \right)$, where $\text{f}\left( r \right)=\frac{1}{r}$, find the sum to $2n$ terms of the series $\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+…$
(ii)
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 $1$.
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