Question

Find the sum of $20$ terms of the series $0.15,0.015,0.0015,...20$

Answer 1

The given G.P. is $0.15,0.015,0.0015,...$
Here, $a=0.15$ and
$r=\frac{0.015}{0.15}=0.1$
$\Rightarrow S_n=\frac{a\left({1-r}^n\right)}{1-r}\therefore S_{20}=\frac{0.15\left[{1-\left(0.1\right)}^{20}\right]}{1-0.1}=\frac{0.15}{0.9}\left[{1-\left(0.1\right)}^{20}\right]=\frac{15}{90}\left[{1-\left(0.1\right)}^{20}\right]=\frac{1}{6}\left[{1-\left(0.1\right)}^{20}\right]$