S_{n + 1} = S_n + \frac{1}{(n + 1)^2} - \frac{1}{(n + 2)^2} = 1 - \frac{1}{(n+1)^2} + \frac{1}{(n + 1)^2} - \frac{1}{(n + 2)^2} = 1 - \frac{1}{((n + 1) + 1)^2}