# 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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