Solutions to Problems 782-792

Q.782 Let $S_n = \frac{1}{1^2-\frac{1}{4}} + \frac{1}{2^2 - \frac{1}{4}}+ \frac{1}{3^2 - \frac{1}{4}} + \cdots + \frac{1}{n^2 - \frac{1}{4}}$. Simply this expression, and show that $n$ is large $S_n$ is approximately equal to 2.