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Let alpha, beta be the roots of x^(2)-x-...

Let `alpha, beta` be the roots of `x^(2)-x-1=0` and `S_(n)=a^(n)+beta^(n)`, for all integers `n ge 1`. Then for every integer `n gt 2`,

A

`S_(n)+S_(n-1)=S_(n+1)`

B

`S_(n)-S_(n-1)=S_(n+1)`

C

`S_(n-1)=S_(n+1)`

D

`S_(n)+S_(n-1)=2S_(n+1)`

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