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Question
Find the sum of the following geometric progression:
1, −1/2, 1/4, −1/8, ... to 9 terms;
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Solution
Here, a = 1 and r = − \[\frac{1}{2}\] .
\[\therefore S_9 = a\left( \frac{1 - r^9}{1 - r} \right) \]
\[ = 1 \left( \frac{1 - \left( - \frac{1}{2} \right)^9}{1 - \left( - \frac{1}{2} \right)} \right) \]
\[ = \frac{1 - \left( - \frac{1}{512} \right)}{\frac{3}{2}}\]
\[ = \frac{\frac{513}{512}}{\frac{3}{2}}\]
\[ = \frac{513 \times 2}{512 \times 3}\]
\[ = \frac{171}{256}\]
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