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_(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)+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=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

For n in N, let a_(n)=sum_(k=1)^(n)2k and b_(n)=sum_(k=1)^(n)(2k-1)* then lim_(n rarr oo)(sqrt(a)_(n)-sqrt(b_(n))) is equal to

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 u_(n)=sum_(k=1)^(n)(k) and v_(n)=sum_(k=1)^(n)(k-0.5) . Then lim_(n rarr oo)(sqrt(u_(n))-sqrt(v_(n))) equals