Chapter 11 - Section 11.2 - Series - 11.2 Exercises - Page 716: 36

Divergent

$\Sigma^{\infty}_{n=1} \frac{1}{1+(\frac{2}{3})^{n}}$ $\lim\limits_{n \to \infty}a_{n} = \lim\limits_{n \to \infty}\frac{1}{1+(\frac{2}{3})^{n}}$ $=\frac{1}{1+0}$ $=1 \ne 0$ Since $\lim\limits_{n \to \infty}a_{n} \ne 0$, the series is divergent.