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If alpha , beta are roots of 375x^(2) - ...

If `alpha , beta `are roots of 375`x^(2) - 25x - 2 = 0 and s_(n) = alpha^(n) + beta^(n)` ,
then `underset(n rarr infty)(lim) sum_(r= 1)^(n) s_(r)` is :

A

`(7)/(116)`

B

`(1)/(12)`

C

`(29)/(358)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • If alpha, beta are roots of 375x^(2) - 25x - 2 = 0 and s_(n) = alpha^(n) + beta^(n), then underset(n rarr infty) sum_(r = 1)^(n) S_(r) is :

    A
    `(7)/(116)`
    B
    `(1)/(12)`
    C
    `(29)/(358)`
    D
    Non of these.

  • If alpha, beta are the roots of x^(2)-a x+b=0 and A_(n)='alpha'^(n)+beta^(n) , then A_(n+1)=

    A
    `aA_(n)+b A_(n-1)`
    B
    `a A_(n)-b A_(n-1)`
    C
    `b A_(n-1)-a A_(n)`
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    `b A_(n)+a A_(n-1)`

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