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=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=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+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))

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 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

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