JEE Math Practice Question

The sum of the series $${1 \over {x + 1}} + {2 \over {{x^2} + 1}} + {{{2^2}} \over {{x^4} + 1}} + ...... + {{{2^{100}}} \over {{x^{{2^{100}}}} + 1}}$$ when x = 2 is :

1. A.$$1 + {{{2^{101}}} \over {{4^{101}} - 1}}$$
2. B.$$1 + {{{2^{100}}} \over {{4^{101}} - 1}}$$
3. C.$$1 - {{{2^{100}}} \over {{4^{100}} - 1}}$$
4. D.$$1 - {{{2^{101}}} \over {{2^{400}} - 1}}$$