$Exercise:$ Find the convergence interval of the series $ \sum_{n = 0}^{\infty} (\frac {x} {1 + x}) ^n.$
$Solution:$ The series is geometric with reason $ \frac {x} {1 + x} $, hence converges if and only if $ | \frac {x} {1 + x} | <1 $ and this happens if and only if, $ | 1- \frac {1} {1 + x} | <1 $, that is, if and only if $ x \in (\frac {-1} {2}, + \infty) $
Is this correct? Thanks so much for reading.