JEE Math Practice 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 :

1. A.$${7 \over {116}}$$
2. B.$${{29} \over {348}}$$
3. C.$${1 \over {12}}$$
4. D.$${{21} \over {346}}$$