Find the sum of each of the following infinite series :
Question:

Find the sum of each of the following infinite series :

$10-9+8.1-\ldots \ldots \infty$

Solution:

It is Infinite Geometric Series

Here, $a=10$

$r=\frac{-9}{10}=-0.9$

$\therefore S u m=\frac{a}{1-r}=\frac{10}{1-(-0.9)}=\frac{10}{1+0.9}=\frac{10}{1.9}=\frac{100}{19}$

Sum $=\frac{100}{19}$