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If `alpha and beta` are the roots of the equation `375 x^(2) - 25x - 2 = 0`, then `underset(n rarr oo r = 1)("lim"overset(n)(Sigma))alpha^(r) + underset(n rarr oo r = 1)("lim" overset(n)(Sigma)) beta^(r)` is equal to :

A

`(21)/(346)`

B

`(29)/(358)`

C

`(1)/(21)`

D

`(7)/(116)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(alpha)/(1-alpha)+(beta)/(1-beta)`
`(alpha(1-beta)+beta(1-alpha))/((1-2)(1-beta))=(alpha+beta-2alphabeta)/(1-alpha-beta+alphabeta)=((25)/(375)-(2(-2))/(375))/(1-(25)/(375)-(2)/(375)=(29)/(375)-(2)/(375))=(29)/(375-27)=(1)/(12)`
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