## Calculus (3rd Edition)

Given $$\sum_{n=1}^{\infty}\frac{2}{3^{n}+3^{-n}}$$ Compare with $\displaystyle\sum_{n=1}^{\infty}\frac{2}{3^{n}}$, which is a convergent series ( geometric with $|r|<1$) and for $n\geq 1$ \begin{align*} 3^{n}+3^{-n} &\geq 3^{n}\\ \frac{1}{3^{n}+3^{-n}} &\leq \frac{1}{3^{n}}\\ \frac{2}{3^{n}+3^{-n}} &\leq \frac{2}{3^{n}} \end{align*} Then $\displaystyle\sum_{n=1}^{\infty}\frac{2}{3^{n}+3^{-n}}$ also converges.