## Calculus (3rd Edition)

We have the given series $\sum_{n=4}^{\infty} \frac{1}{n^{2}-9}$ We apply the limit comparison test with $b_n=(\frac{1}{n^2})$ (a convergent p-series with $p=2\gt 1$): $L=\lim_{n\rightarrow\infty} \frac{1}{n^{2}-9}\times n^2=\lim_{n\rightarrow\infty}\frac{n^2}{n^{2}-9}=1$ Since $L=1$, our starting series converges.