Find the sum of the first 9 terms of the geom | vedclass

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(C) The given series is a geometric progression with first term $a = 1$ and common ratio $r = -\frac{1}{2}$.The sum of the first $n$ terms of a geomet

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$171/256$

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(C) The given series is a geometric progression with first term $a = 1$ and common ratio $r = -\frac{1}{2}$.The sum of the first $n$ terms of a geometric progression is given by $S_n = \frac{a(1 - r^n)}{1 - r}$.For $n = 9$,$S_9 = \frac{1(1 - (-1/2)^9)}{1 - (-1/2)}$.$S_9 = \frac{1 - (-1/512)}{1 + 1/2} = \frac{1 + 1/512}{3/2}$.$S_9 = \frac{513/512}{3/2} = \frac{513}{512} 	imes \frac{2}{3}$.$S_9 = \frac{171}{256}$.

Find the sum of the first $9$ terms of the geometric series $1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{8} + \dots$

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