For `n in N` ,let `a_n=sum_(k=1)^n2k and b_n=sum_(k=1)^n(2k-1)`.then `lim_(n->oo)(sqrt(a)_n-sqrt(b_n))` is equal to

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

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

If S_n=sum_(k=1)^n a_k and lim_(n->oo)a_n=a , then lim_(n->oo)(S_(n+1)-S_n)/sqrt(sum_(k=1)^n k) is equal to

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

If S_(n),=sum_(k=1)^(n)a_(k) and lim_(n rarr oo)a_(n)=a, then lim_(n rarr oo),(S_(n+1)-S_(n))/(sqrt(sum_(k=1)^(n)k)) is equal to

If a,b in R^(+) then find Lim_(nrarroo) sum_(k=1)^(n) ( n)/((k+an)(k+bn)) is equal to

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .