JEE Math Practice Question

If 0 < a, b < 1, and tan$$-$$1a + tan$$-$$1b = $${\pi \over 4}$$, then the value of $$(a + b) - \left( {{{{a^2} + {b^2}} \over 2}} \right) + \left( {{{{a^3} + {b^3}} \over 3}} \right) - \left( {{{{a^4} + {b^4}} \over 4}} \right) + .....$$ is :

1. A.$${\log _e}$$2
2. B.e
3. C.$${\log _e}\left( {{e \over 2}} \right)$$
4. D.e2 = 1