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Question
Find the sum of the following geometric progression:
4, 2, 1, 1/2 ... to 10 terms.
Solution
Here,a = 4 and r = \[\frac{1}{2}\]
\[\therefore S_n = a\left( \frac{1 - r^{10}}{1 - r} \right)\]
\[ = 4\left( \frac{1 - \left( \frac{1}{2} \right)^{10}}{1 - \left( \frac{1}{2} \right)} \right)\]
\[ = 4\left( \frac{1 - \left( \frac{1}{1024} \right)}{\frac{1}{2}} \right)\]
\[ = 8\left( 1 - \frac{1}{1024} \right)\]
\[ = \frac{1023}{128}\]
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