Powers of 1/a

Algebra Level 3

S=1+2(15)+3(15)2+4(15)3. S = 1 + 2\left(\frac{1}{5}\right) + 3\left(\frac{1}{5}\right)^2 + 4\left(\frac{1}{5}\right)^3 \ldots .

If S=abS = \frac{a}{b}, where aa and bb are coprime positive integers, what is the value of a+ba+b?

Details and assumptions

SS is obtained as the sum of infinitely many terms. The nnth term is n(15)n1 n\left(\frac{1}{5}\right)^{n-1} .


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