Find $\sum\limits_{r=1}^{n}{\frac{1}{r(r+2)}}$ in terms of $n$. Give a reason why $\sum\limits_{r=1}

Question

Find $\sum\limits_{r=1}^{n}{\frac{1}{r(r+2)}}$ in terms of $n$. Give a reason why $\sum\limits_{r=1}^{\infty }{\frac{1}{r(r+2)}}$ converges and write down its value.

Accepted Answer

(i) ½[3/2 - 1/(n+1) - 1/(n+2)] (ii) 3/4

Application of Sum to Infinity Q1

Application of Sum to Infinity Q1

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