If $\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$. is a G.P then $\mathrm{S}_{\mathrm{n}}=$

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Professor PC Thomas Classes · Answer

First term $a=1/3$, ratio $r=1/3$. $S_n = \frac{a(1-r^n)}{1-r} = \frac{\frac{1}{3}(1-(1/3)^n)}{2/3} = \frac{1}{2}(1-\frac{1}{3^n})$.