`sum_(n=1)^(oo)((1)/(4n-3)-(1)/(4n-1))=(pi)/(n)` find `n`

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

sum_(n=1)^(oo)((4n+5).5^(-n))/(n(5n+5))=

sum_(0)^(oo)(1)/((3n+1)(3n+2))

The value of lim_(n rarroo) sum_(r=1)^(n)(1)/(sin{((n+r)pi)/(4n)}).(pi)/(n) is equal to

sum_(n=3)^(oo)(1)/(n^(5)-5n^(3)+4n)(A)(1)/(120) (B) (1)/(96)(C)(1)/(24) (D) (1)/(144)

If S=sum_(n=2)^(oo)(3n^(2)+1)/((n^(2)-1)^(3)) then (9)/(4S) is

Find sum_(n=1)^(oo)cot^(-1)(2*n^(2))=

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))

If sum_(n=0)^(oo)2cot^(-1)((n^(2)+n+4)/(2))=k pi then find the value of k

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