# How do you find the sum of the infinite geometric series with a_1=-5 and r=1/6?

A geometric series of first term $a$ and common ratio $r$ is divergent if $| r | \ge 1$, and convergent if $| r | < 1$, in which case the sum is given by the formula $\frac{a}{1 - r}$. In the present case $r = \frac{1}{6}$ is less than 1 in absolute value, so that the series is convergent and its sum is $- \frac{5}{1 - \left(\frac{1}{6}\right)} = - 6$. See Geometric Series