Question

Find the sum of the infinite G.P. 2, $\frac{2}{3}$, $\frac{2}{9}$, $\frac{2}{27}$ . . . . .

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Answer 1

S = 2 + $\frac{2}{3}$ + $\frac{2}{3^2}$ + $\frac{2}{3^3}$.............. --------------(1)

$\frac{S}{3}$ = $\frac{2}{3}$ + $\frac{2}{3^2}$ + ............... ----------------(2)

(1) - (2) $\Rightarrow$ S $\times$ $\frac{2}{3}$ = 2

$\Rightarrow$ S = 3