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# Consider the geometric series . If the sum is a perfect square, what is the smallest possible value of where is a positive

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Consider the geometric series  $4+\frac{12}{a}+\frac{36}{a^2}+\cdots$. If the sum is a perfect square, what is the smallest possible value of  where  is a positive integer?

Guest Jun 23, 2018
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4+∑[4*3^n/a^n], n=1 to infinty=16, where a=4

Guest Jun 23, 2018