`sum_(n=1)^oo(tan^-1((4n)/(n^4-2n^2+2)))` is equal to (A) `tan ^-1 (2)+tan^-1 (3)` (B) `4tan^-1 (1)` (C) `pi/2` (D) `sec^-1(-sqrt2)`

sum_(n=1)^(oo)tan^(-1)((8)/(4n^(2)-4n+1)) is equal to

The sum sum_(n=1)^oo tan^(-1)(3/(n^2+n-1)) is equal to

The sum sum_(n=1)^(oo)tan^(-1)((3)/(n^(2)+n-1)) is equal to

sum_(r=1)^(n) tan^(-1)(2^(r-1)/(1+2^(2r-1))) is equal to a) tan^(-1)(2^n) b) tan^(-1)(2)^n-pi/4 c) tan^(-1)(2^(n+1)) d) tan^(-1)(2^(n+1))-pi/4

The sum sum_(n=1)^(60)tan^(-1)((2n)/(n^(4)-n^(2)+1)) equals tan^(-1)K, where K equal-

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

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

sum_(r=1)^nsin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1)))) is equal to (a) tan^(-1)(sqrt(n))-pi/4 (b) tan^(-1)(sqrt(n+1))-pi/4 (c) tan^(-1)(sqrt(n)) (d) tan^(-1)(sqrt(n)+1)