# Is the geometric series 10 - 6 + 3.6 - 2.16 + ... convergent or divergent?

May 6, 2016

Convergent series whose sum is $6.25$

#### Explanation:

In the series $10 - 6 + 3.6 - 2.16 + \ldots .$

first term $a$ is $10$ and ratio $r$ of a term and its preceding term is $- \frac{6}{10} = \frac{3.6}{-} 6 = - \frac{2.16}{3.6} = - 0.6$

Hence it is a geometric series. If in such case $| r | < 1$, the series is convergent and the sum of an infinite geometric series is given by

$\frac{a}{1 - r} = \frac{10}{1 - \left(- 0.6\right)} = \frac{10}{1.6} = \frac{10 \times 10}{16} = \frac{25}{4} = 6.25$