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

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

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

Let U_(n)=sum_(k=1)^(n)(n)/(n^(2)+k^(2)),S_(n)=sum_(k=0)^(n-1)(n)/(n^(2)+k^(2)) then

S_(n)=sum_(k=1)^(n)(k^(2)+n^(2))/(n^(3)) and T_(n)=sum_(k=0)^(n-1)(k^(2)+n^(2))/(n^(3)),n in N then

If f(x) = (a^(x))/(a^(x) + sqrt(a)), a gt 0 prove that (i) f(x) + f(1-x) = 1 (ii) underset(k=1)overset(2n-1)sum 2f ((k)/(2n)) = 2n-1 (iii) underset(k=1)overset(2n)sum 2f((k)/(2n+1)) = 2n

If underset(k=0)overset(n)(sum)(k^(2)+k+1)k! =(2007).2007! , then value of n is

The value of cot[underset(n=1)overset(100)Sigmacot^(-1)(1+underset(k=1)overset(n)Sigma2k)] is

Let S_(n)=sum_(k=1)^(4n)(-1)^((k(k+1))/2)k^(2) . Then S_(n) can take values