Given that $\sum\limits_{r=2}^{n}{\frac{1}{{{r}^{2}}-1}}=\frac{3}{4}-\frac{1}{2n}-\frac{1}{2\left( n

Question

Given that $\sum\limits_{r=2}^{n}{\frac{1}{{{r}^{2}}-1}}=\frac{3}{4}-\frac{1}{2n}-\frac{1}{2\left( n+1 \right)}$, state $\sum\limits_{r=2}^{\infty }{\frac{1}{{{r}^{2}}-1}}$, find $\sum\limits_{r=2}^{n-1}{\frac{1}{r(r+2)}}$.

Accepted Answer

$\dfrac{5}{12} - \dfrac{1}{2n} - \dfrac{1}{2(n+1)}$

2017 EJC Promo Q7 (b) [Modified]

2017 EJC Promo Q7 (b) [Modified]

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