The minimum number of terms of the series $1+3+9+27+\ldots$ so that the sum may exceed 1000 is

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Professor PC Thomas Classes · Answer

$S_n = \frac{1(3^n - 1)}{3-1} > 1000 \Rightarrow 3^n > 2001$. $3^6=729$, $3^7=2187$. Minimum terms $n=7$.