## Calculus (3rd Edition)

Given $$\sum_{n=3}^{\infty} \frac{3 n+5}{n(n-1)(n-2)}$$ Compare with the convergent series $\displaystyle \sum_{n=3}^{\infty}\frac{1}{n^{2}}$ ($p-$series , p>1) and by using the Limit Comparison Test, we get: \begin{align*} \lim_{n\to \infty} \frac{a_n}{b_n}&=\lim_{n\to \infty} \frac{3 n^2(n+5)}{n(n-1)(n-2)}\\ &=3 \end{align*} Then $\displaystyle \sum_{n=3}^{\infty}\frac{3 n+5}{n(n-1)(n-2)}$ also converges