`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

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

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

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

Let S_n=sum_(k=0)^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 (a) S_n lt pi/3sqrt(3) b) S_n gt pi/3sqrt(3) (c) T_n lt pi/3sqrt(3) (d) T_n gt pi/3sqrt(3)

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

Let S_n=sum_(k=0)^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(correct options may be more than one) (a) S_n lt pi/(3sqrt(3)) b) S_n gt pi/(3sqrt(3)) (c) T_n lt pi/(3sqrt(3)) (d) T_n gt pi/(3sqrt(3))

Given S_(n)=sum_(k=1)^(n)(k)/((2n-2k+1)(2n-k+1)) and T_(n)=sum_(k=1)^(n)(1)/(k) then (T_(n))/(S_(n)) 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

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