JEE Math Practice Question

If $$A = \sum\limits_{n = 1}^\infty {{1 \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}} $$ and $$B = \sum\limits_{n = 1}^\infty {{{{{( - 1)}^n}} \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}} $$, then $${A \over B}$$ is equal to :

1. A.$${{11} \over 9}$$
2. B.1
3. C.$$-$$$${{11} \over 9}$$
4. D.$$-$$$${{11} \over 3}$$