By use of the Squeeze Theorem calculate the limit $ \lim\limits_{n \to \infty } \frac{1}{n^2+1} + \frac{1}{n^2+2} + \cdots + \frac{1}{n^2+n} $.
By use of the Squeeze Theorem calculate the limit $ \lim\limits_{n \to \infty } \frac{1}{n^2+1} + \frac{1}{n^2+2} + \cdots + \frac{1}{n^2+n} $.