Calculus 10th Edition

Th.9.6 Convergence of a Geometric Series: A geometric series with ratio $r$ diverges when $|r| \geq 1$. If $0 \lt |r| \lt 1$, then the series converges to the sum $\displaystyle \sum_{n=0}^{\infty}ar^{n}=\frac{a}{1-r},\quad 0 \lt |r| \lt 1$. ------------ $\displaystyle \sum_{n=0}^{\infty}(\frac{7}{6})^{n}$ is a geometric series, with $r=\displaystyle \frac{7}{6} \gt 1$ By Th.9.6, the series diverges.