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

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

(ii) $\frac{3}{4}$ (iii) $\frac{5}{12}-\frac{1}{2n}-\frac{1}{2\left( n+1 \right)}$

2017 EJC Promo Q7 [Modified]

2017 EJC Promo Q7 [Modified]

Video Solution:

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