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)(1)/(2n(2n+1))=

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

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

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

If x= sum_(n=0)^oo (Costheta)^(2n) , y= sum_(n=0)^oo (Sinphi)^(2n) , z= sum_(n=0)^oo (Cosphi)^(2n). (Sintheta)^(2n) Then which of the following is true ??

Find sum_(n=1)^oo (0.4)^n

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

sum_(n=0)^( oo) (-1)^(n) x^( n+1)=