Answer
convergent, sum=$\displaystyle \frac{5}{7}$
Work Step by Step
An infinite geometric series is a series of the form
$ a+ar+ar^{2}+ar^{3}+\cdots+ar^{n-1}+\cdots$
An infinite geometric series for which $|r| < 1$
has the sum $S=\displaystyle \frac{a}{1-r}$
If $|r| \geq 1$, the series diverges (the sum does not exist).
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$a=1$
$r=-\displaystyle \frac{2}{5}, \quad |r| < 1,$
so the series is convergent,
$S=\displaystyle \frac{a}{1-r}=\frac{1}{1-(-\frac{2}{5})}=\frac{1}{\frac{5+2}{5}}=\frac{5}{7}$
