# Question #f239c

Sep 21, 2017

$0.878787 \ldots \implies \frac{87}{100} + \frac{87}{10000} + \frac{87}{1000000} + \ldots$

Hence, 1st term $a = \frac{87}{100}$ and common ratio $r = \frac{1}{100}$

Now, ${S}_{\infty} = \frac{a}{1 - r}$

i.e. $\frac{a}{1 - \frac{1}{100}} = \frac{100 a}{99}$

So, with $a = \frac{87}{100}$ we have:

$\left(\frac{100}{99}\right) \left(\frac{87}{100}\right) = \frac{87}{99}$

or, $\frac{29}{33}$

:)>