# Not Limiting a Sum

Algebra Level 4

$\alpha, \beta$ are the roots of $375x^2-25x-2=0$. Denote $S_n = \alpha^n+\beta^n$, and if the summation below is in the form of $\frac a b$ where $a,b$ are coprime positive integers. Find the value of $a+b$.

$\large \displaystyle \sum_{n=1}^\infty S_n$

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