If $\alpha $ and $\beta $ are the roots of the equation 375x2 – 25x – 2 = 0, then $\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{\alpha ^r}} + \mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{\beta ^r}} $ is equal to :

Question

If $\alpha $ and $\beta $ are the roots of the equation 375x² – 25x – 2 = 0, then $\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{\alpha ^r}} + \mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{\beta ^r}} $ is equal to :

${7 \over {116}}$

${{29} \over {348}}$

${1 \over {12}}$

${{21} \over {346}}$

Solution

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