" (2) "tan^(-1)(2)/(4)+tan^(-1)(2)/(9)+tan^(-1)(2)/(16)+..." to n terms."

tan^(-1)(1)/(4)+tan^(-1)(2)/(9)=tan^(-1)(1)/(2)

tan^(-1)((1)/(4))+tan^(-1)((2)/(9))=tan^(-1)((1)/(2))

tan^(- 1)(1/4)+tan^(- 1)(2/9)=1/2tan^(- 1)(4/3)

tan^(- 1)(1/4)+tan^(- 1)(2/9)=1/2tan^(- 1)(4/3)

The value of tan^(-1)((1)/(3))+tan^(-1)((2)/(9))+tan^(-1)((4)/(33))+tan^(-1)((8)/(129))+...n terms is:

2 ( tan ^(-1)""(1)/(4) +tan ^(-1)""(2)/(9))=cos ^(-1)""(3)/(5)

Sum the series, 'n' terms tan^(-1) 2/4 +tan^(-1) 2/9+tan^(-1) 2/16+ tan^(-1) 2/25+.... to 'n' terms. Also show that S_(n)=tan^(-1)3

The sum of the infinite terms of the series "tan"^(-1)((1)/(3))+ "tan"^(-1)((2)/(9)) + tan^(-1)((4)/(33)) + .... is equal to (pi)/(n) The value of n is:

The sum of the infinite terms of the series "tan"^(-1)((1)/(3))+ "tan"^(-1)((2)/(9)) + tan^(-1)((4)/(33)) + .... is equal to (pi)/(n) The value of n is: