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Find the infinite sum of
\( \frac{1}{7} + \frac{2}{7^2} + \frac{1}{7^3} + \frac{2}{7^4} + \cdots\)

 Dec 3, 2021
 #1
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1)  Divide this into two infinite geometric series:

            1/7  +  1/73  +  1/75  + ...

     and

             2/72  +  2/74  +  2/76  + ...

 

2)  Find the sum of each part, using this formula:  Sum  =  a / (1 - r)

 

3)  Add the two sums together to find the final result.

 Dec 4, 2021

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