2022 RI Promo Q4
(i)
Find $\sum\limits_{r=1}^{n}{\frac{1}{\left( r+1 \right)\left( r+3 \right)}}$, where $n\ge 3$. (There is no need to express your answer as a single algebraic fraction.)
[5]
(ii)
Explain why $\sum\limits_{r=1}^{\infty }{\frac{1}{\left( r+1 \right)\left( r+3 \right)}}$ is a convergent series, and state the value of the sum to infinity.
[2]
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