[qquad f(n)=tan^(-1)((4)/(1+3.4))+tan^(-1)((6)/(1+8.9))],[+tan^(-1)((8)/(1+15.16))+...n]

Sum the series: tan ^ (- 1) ((4) / (1 + 3.4)) + tan ^ (- 1) ((6) / (1 + 8.9)) + tan ^ (- 1) ((8) /(1+15.16))+......oo

Find - tan^(-1)((3)/(4))+tan^(-1)((3)/(5))-tan^(-1)((8)/(19))=

tan^(-1)((3)/(4))+tan^(-1)((3)/(5))-tan^(-1)((8)/(19))=

Sum the series : tan^(- 1)(4/(1+3.4))+tan^(- 1)(6/(1+8.9))+tan^(- 1)(8/(1+15.16))+............oo is :

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

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

tan ^ (- 1) ((3) / (4)) + tan ^ (- 1) ((3) / (5)) + tan ^ (- 1) ((8) / (19))

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

Prove that tan^(-1)((1)/(2))+tan^(-1)((1)/(5))+tan^(-1)((1)/(8))=(pi)/(4)

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