sum_(n=1)^(oo)tan^(-1)((4n)/(n^(4)-2n^(2)+2))" equals "

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)(-sqrt(2))

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

If x_(0)=sum_(n=1)^(oo)tan^(-1)((4n)/(n^(4)-2n^(2)+3)), then which of the following is/are correct

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

sum_(n=1)^(oo)(1)/(2n(2n+1))=

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