Rationalise a radical sum and distinguish terms from partial sums

Given $\sum_{n=1}^N(\sqrt{n+1}-\sqrt{n-1})=\sqrt N+\sqrt{N+1}-1$:

(i) Find exactly (a) $\sum_{n=50}^{100}(\sqrt{n+1}-\sqrt{n-1})$ 2 marks, and (b) $\sum_{n=50}^{100}1/(\sqrt{n+1}+\sqrt{n-1})$.1 mark

(ii) State with a reason whether $\sum_{n=1}^{\infty}(\sqrt{n+1}-\sqrt{n-1})$ converges.1 mark