`sum_(n=1)^ntan^(- 1)(n/n)`

The value of the lim_(n->oo)tan{sum_(r=1)^ntan^(- 1)(1/(2r^2))} is equal to

The value of the lim_(n->oo)tan{sum_(r=1)^ntan^(- 1)(1/(2r^2))} is equal to

Prove that: sum_(m=1)^ntan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2+n+2))

Prove that: sum_(m=1)^ntan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2+n+2))

lim_(n->oo) sum_(r=1)^ntan^(- 1)((2r+1)/(r^4+2r^3+r^2+1)) is equal to

sum_(m-1)^ntan^(-1)((2m)/(m^4+m^2+2)) is equal to (a) tan^(-1)((n^2+n)/(n^2+n+2)) (b) tan^(-1)((n^2-n)/(n^2-n+2)) (c) tan^(-1)((n^2+n+2)/(n^2+n)) (d) none of these

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

Let S_(n)=sum_(r=1)^(oo)(1)/(n^(r)) and sum_(n=1)^(k)(n-1)S_(n)=5050, then k=