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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?

 Jun 27, 2022
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The common  ratio  =  5/a

 

The  sum  =          4 / ( 1 -5/a)  =  (4)  /  [ ( a - 5) / a ] =     (4a) / (a - 5)

 

The smallest integer value of  a  that produces a perfect square is when   a =   9

 

 

cool cool cool  

 Jun 27, 2022

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