# How do you find the sum of the convergent series 10-5/2+5/8-...? If the convergent series is not convergent, how do you know?

Nov 23, 2015

Yes, it is convergent because $\left\mid r \right\mid < 1$

#### Explanation:

$r = \frac{- \frac{5}{2}}{10} = - \frac{1}{4}$

$\left\mid - \frac{1}{4} \right\mid < 1$, so it is convergent

$\text{infinite geometric sum} = {a}_{1} / \left(1 - r\right) = \frac{10}{1 - \left(- \frac{1}{4}\right)} = 8$

hope that helped