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The sum of the first $n$ terms in the infinite geometric sequence $\left\{\frac{1}{4},\frac{1}{8},\frac{1}{16},\dots \right\}$ is $\frac{255}{512}$. Find $n$.

 Aug 29, 2020
 #1
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n = 18.

 Aug 29, 2020
 #2
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The sequence is:

 

1/4, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256, 1/512 = 255 / 512

 

So, n = 8

 Aug 29, 2020

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