2024 CJC Promo Q3

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

1. Find \(\sum_{r=5}^{n+1} \frac{1}{r(r+1)}\).[3]
2. 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]