It is given that $\sum_{r=1}^{n} \frac{1}{r(r+1)} = 1 - \frac{1}{n+1}$. Find \(\sum_{r=5}^{n+

Question

It is given that $\sum_{r=1}^{n} \frac{1}{r(r+1)} = 1 - \frac{1}{n+1}$. Find $\sum_{r=5}^{n+1} \frac{1}{r(r+1)}$.[3] Give a reason why the series in part (a) is convergent and state the value of $\sum_{r=5}^{\infty} \frac{1}{r(r+1)}$.[2]

Accepted Answer

(a) ${\frac{1}{5} - \frac{1}{n+2}}$ (b) ${\frac{1}{5}}$

2024 CJC Promo Q3

2024 CJC Promo Q3