The sum to infinite terms of the series `cot^(- 1)(2^2+1/2)+cot^(- 1)(2^3+1/(2^2))+cot^(- 1)(2^4+1/(2^3))+...` is

Find the sum to n terms of the series S_(n)=cot^(-1)(2^(2)+(1)/(2))+cot^(-1)(2^(3)+(1)/(2^(2)))+cot^(-1)(2^(4)+(1)/(2^(3)))+..... upto n terms ?

The sum of the infinite terms of the series cot^(-1)(1^2+3/4)+cot^(-1)(2^2+3/4)+cot^(-1)(3^2+3/4)+...+oo is equal to a. tan^(-1)(1) b. tan^(-1)\ \ (2) c. tan^(-1)2\ d. (3pi)/4-tan^(-1)3

If the sum of first 16 terms of the series s=cot^(-1)(2^(2)+(1)/(2))+cot^(-1)(2^(3)+(1)/(2^(2)))+cot^(-1)(2^(4)+(1)/(2^(3)))+ up to terms is cot^(-1)((1+2^(n))/(2(2^(16)-1))), then find the value of n.

Sum of infinite terms of the series cot^(-1) ( 1^(2) + 3/4) + cot^(-1) ( 2^(2) + 3/4) + cot^(-1) ( 3^(2) + 3/4) + ... is

Sum to infinite terms the series: cot^-1(1^2+ 3/4)+cot^-1 (2^2+3/4)+cot^-1 (3^2+3/4)+….

The sum of the series cot^(-1)((9)/(2))+cot^(-1)((33)/(4))+cot^(-1)((129)/(8))+…….oo is equal to :

The sum of the series cot^(-1)((9)/(2))+cot^(-1)((33)/(4))+cot^(-1)((129)/(8))+…….oo is equal to :

sin[(1)/(2)cot^(-1)((2)/(3))] =

The sum to infinite terms of the series tan^(-1)((2)/(1-1^(2)+1^(4)))+tan^(-1)((4)/(1-2^(2)+2^(4)))+tan^(-1)((6)/(1-3^(2)+3^(4)))+