If `(tan^(- 1)(1/3)+tan^(- 1)(1/7)+tan^(- 1)(1/13)+......+tan^(- 1)(1/381))=m/n` where `m,n in N`, then find least value of `(m+n)`.

tan^(-1)(n+1)+tan^(-1)(n-1)=tan^(-1)(8/31)

"tan"^(-1)1/3+"tan"^(-1)1/7+……+tan^(-1)(1/(n^(2)+n+1))=

Prove that tan^(- 1)(1/3)+tan^(- 1)(1/7)+tan^(- 1)(1/13)+..........+tan^-1 (1/(n^2+n+1))+......oo = pi/4

Prove that tan^(- 1)(1/3)+tan^(- 1)(1/7)+tan^(- 1)(1/13)+..........+tan^-1 (1/(n^2+n+1))+......oo =pi/4

Prove that tan^(- 1)(1/3)+tan^(- 1)(1/7)+tan^(- 1)(1/13)+..........+tan^-1 (1/(n^2+n+1))+......oo =pi/4

tan^(-1)n+cot^(-1)(n+1)=tan^(-1)(n^(2)+n+1)

If tan^(-1)(1/(1+1. 2))+tan^(-1)(1/(1+2. 3))+.... +tan^(-1)(1/(1+n.(n+1)))=tan^(-1)theta, then find the value of thetadot

If theta=tan^(-1)((1)/(10))+tan^(-1)((1)/(9))+...+tan^(-1)(1)+tan^(-1)(2)+...+tan^(-1)(10)+tan^(-1)(11) .If tan theta=(m)/(n) (where m,n are coprime) then the value of (m+n) is equal to

tan^(-1)((1)/(1+1.2))+tan^(-1)((1)/(1)+2.3)+...+tan^(-1)((1)/(1+n(n+1)))=tan^(-1)theta then find the value of theta.