$B=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{30}}$
$⇒5B=1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{29}}$
$⇒5B-B=(1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{29}})-(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{30}})$
$⇒4B=1-\frac{1}{5^{30}}$
$⇒B=\frac{1}{4}-\frac{1}{5^{30}.4}$.