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 :

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 :

${\log _e}$2

${\log _e}\left( {{e \over 2}} \right)$

e² = 1

Solution

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