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# Find the sum of $20$ terms of the G.P., $0.15,0.015,0.0015................$

$\begin{array}{1 1} \large\frac{1-(0.1)^{20}}{6} \\\large\frac{1-(0.1)^{20}}{60} \\ \large\frac{1-(0.1)^{20}}{3} \\ \large\frac{1-(0.1)^{20}}{30} \end{array}$

Toolbox:
• Sum of $n$ terms of a G.P$=S_n=a.\large\frac{1-r^n}{1-r}$
Given G.P. is $0.15+0.015+0.0015..........upto\:20\:terms$
In this G.P. $a=0.15\:\;and$ common ratio $r=\large\frac{0.015}{0.15}=\frac{1}{10}$$=0.1 We know that sum of n terms of a G.P.=S_n=a.\large\frac{1-r^n}{1-r} \therefore\:S_{20}=0.15\times \large\frac{1-(0.1)^{20}}{1-0.1} =0.15\times\large\frac{1-(0.1)^{20}}{0.9} =\large\frac{1}{6}$$\times (1-(0.1)^{20})$