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α,β\alpha, \betaα,β are the roots of 375x2−25x−2=0375x^2-25x-2=0 375x2−25x−2=0. Denote Sn=αn+βn S_n = \alpha^n+\beta^n Sn=αn+βn, and if the summation below is in the form of ab \frac a b ba where a,ba,ba,b are coprime positive integers. Find the value of a+ba+ba+b.
∑n=1∞Sn\large \displaystyle \sum_{n=1}^\infty S_n n=1∑∞Sn
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