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Consider the geometric series 4 + 20/a + 100/a^2 + .... If the sum is a perfect square, what is the smallest possible value of a where is a positive integer?

 Dec 2, 2020
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The common ratio  is    5/a

 

The sum is

 

     4                     4a

_______  =       _____  

1  -  5/a              a -  5

 

Note  that when a   = 9

 

4(9)             36

____ =    _______  =     9   = perfect square

9 - 5             4

 

 

cool cool cool

 Dec 2, 2020

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