If 0 < a, b < 1, and tan⁻¹a + tan⁻¹b = (π)/4, then the value of (a + b) - ((a² + b²)/2) + ((a³ + b³)/3) - ((a⁴ + b⁴)/4) +..... is:

Trigonometry: JEE Main 2021 Mathematics question

JEE Main 2021 · 26 Feb, Evening shift · Q4101

JEE Main 202126 Feb, Evening shiftMathematicsMediumTrigonometry118× since 2002

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 :

JEE Main 2021 · 26 Feb, Evening shift · Q4101

JEE Main 202126 Feb, Evening shiftMathematicsMediumTrigonometry118× since 2002

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 :