Find the sum of G.P. :

0.3 + 0.03 + 0.003 + 0.0003 + …… to 8 terms.

Common ratio (r) = $\dfrac{0.03}{0.3}$ = 0.1

$S = \dfrac{a(1 - r^n)}{(1 - r)} ……….(As |r| \lt 1)\\[1em] = \dfrac{0.3\Big[1 - (0.1)^8\Big]}{1 - 0.1} \\[1em] = \dfrac{0.3\Big[1 - \Big(\dfrac{1}{10}\Big)^8\Big]}{0.9} \\[1em] = \dfrac{1}{3}\Big(1 - \dfrac{1}{10^8}\Big).$

Hence, sum = $\dfrac{1}{3}\Big(1 - \dfrac{1}{10^8}\Big)$.