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The sum of the first n terms in the infinite geometric sequence 1/4, 1/8, 1/16, ... is \(15/32\). Find n.

 Jan 28, 2022
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First we can see that the sum of the first n terms ends with a denominator of 32.

 

If the denominator multiplies by 2 every time, then we know the last term has a denominator of 32.

 

Thus n = 4.

 

This is true because the first term can be 8/32, second term is 4/32, third term is 2/32, and the fourth term is 1/32,

adding up the four terms is 15/32, so there are 4 terms, and that is the explanation why n = 4.

 

smiley

 Jan 28, 2022
edited by proyaop  Jan 28, 2022

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