That's big

Algebra Level 3

If \(\alpha ,\beta \) be roots of the equation \(35x^{2}-140x+140=0\) and \(S_{n}={ \alpha }^{ 100n }-{ \beta }^{ 100n }\). Find \[\sum_{ i=1 }^{ \infty }{ (S_{i}\times S_{i-1}) }\]

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