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) (1)/(2n(2n+1)) is equal to

The value of sum_(n=1)^(oo)(1)/(2n(2n+1)) is equal to

sum_(n=0)^(oo) (n^(2) + n + 1)/((n +1)!) is equal to

The sum of the series sum_(n=1)^oo(n^2+6n+10)/((2n+1)!) is equal to

The infinite sum sum_(n=1)^(oo) ((5^(n) + 3^(n))/(5^(n))) is equal to

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

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)

lim_(x to oo ) tan { sum_(r=1)^(n) tan^(-1) ((1)/( 1 +r +r^2))} is equal to ________.