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Q.

If $α, β$ are the roots of the equation $375 x^{2} - 25 x - 2 = 0$ then $\underset{n \to \infty}{L i m} \sum_{r = 1}^{n} α^{r} + \underset{n \to \infty}{L i m} \sum_{r = 1}^{n} β^{r}$ is equal to

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a

$\frac{21}{346}$

b

$\frac{29}{358}$

c

$\frac{7}{116}$

d

$\frac{1}{12}$

answer is A.

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Detailed Solution

Given

$= \frac{α}{1 - α} + \frac{β}{1 - β} = \frac{(α + β) - 2 α β}{1 - (α + β) + α β} = \frac{29}{348} = \frac{1}{12}$

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