If 2^{10} + 2^{9} cdot 3^{1} + 2^{8} cdot 3^{ | vedclass

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Question

(C) The given expression is a Geometric Progression ($G$.$P$.) with $n = 11$ terms.Here,the first term $a = 2^{10}$ and the common ratio $r = \frac{3}

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$3^{11}$

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(C) The given expression is a Geometric Progression ($G$.$P$.) with $n = 11$ terms.Here,the first term $a = 2^{10}$ and the common ratio $r = \frac{3}{2}$.The sum of a $G$.$P$. is given by $S_n = a \frac{r^n - 1}{r - 1}$.Substituting the values: $S' = 2^{10} \cdot \frac{(\frac{3}{2})^{11} - 1}{\frac{3}{2} - 1}$.$S' = 2^{10} \cdot \frac{\frac{3^{11}}{2^{11}} - 1}{\frac{1}{2}} = 2^{11} \cdot (\frac{3^{11} - 2^{11}}{2^{11}})$.$S' = 3^{11} - 2^{11}$.Given that $S' = S - 2^{11}$,we have $3^{11} - 2^{11} = S - 2^{11}$.Therefore,$S = 3^{11}$.

If $2^{10} + 2^{9} \cdot 3^{1} + 2^{8} \cdot 3^{2} + \ldots + 2^{0} \cdot 3^{10} = S - 2^{11}$,then $S$ is equal to

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