If , are roots of the equation 375x^2-25x-2=0 and S_n= ^n+ ^n, then _ n _ r=1 ^nS_r is equal to

JEE Main Mathematics question

If are roots of the equation and , then is equal to

Answer: (C)

and , and , so the geometric series converge: the limit is . This equals

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Question ID VK-014130