Let `S_(n)=underset(k=1)overset(n)sum (n)/(n^(2)+nk+k^(2)) and T_(n)=underset(k=0)overset(n-1)sum(n)/(n^(2)+nk+k^(2))` for `n=1, 1,2,3...,` they

underset(n=1)overset(oo)sum(x^(n))/(n+2)=

Let S_(n)=sum_(k=1)^(n) (n)/(n^(2)+nk+k^(2)) and T_(n)=sum_(k=0)^(n-1)(n)/(n^(2)+nk+k^(2)) for n= 1,2,3..., then

underset(n=1)overset(oo)sum(n^(2))/((n+1)!)=

Let S_(n)=sum_(k=1)^(n)n/(n^(2)+kn+k^(2)) and T_(n)=sum_(k=0)^(n-1)n/(n^(2)+kn+k^(2)) for n=1,2,3, ………. Then

If k=underset(r=0)overset(n)(sum)(1)/(.^(n)C_(r)) , then underset(r=0)overset(n)(sum)(r)/(.^(n)C_(r)) is equal to

If S_(n) = underset (r=0) overset( n) sum (1) /(""^(n) C_(r)) and T_(n) = underset(r=0) overset(n) sum (r )/(""^(n) C_(r)) then (t_(n))/(s_(n)) =

If S_(n) = underset (r=0) overset( n) sum (1) /(""^(n) C_(r)) and T_(n) = underset(r=0) overset(n) sum (r )/(""^(n) C_(r)) then (t_(n))/(s_(n)) = ?

The value of cot (underset(n=1)overset(23)sum cot^(-1) (1 + underset(k=1)overset(n)sum 2k)) is

The value of cot (underset(n=1)overset(23)sum cot^(-1) (1 + underset(k=1)overset(n)sum 2k)) is