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

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

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 be a sequence such that lim_(x rarr oo)a_(n)=0. Then lim_(n rarr oo)(a_(1)+a_(2)++a_(n))/(sqrt(sum_(k=1)^(n)k)), is

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

The value of lim_(n->oo) sum_(k=1)^n log(1+k/n)^(1/n) ,is

The value of lim_(n->oo) sum_(k=1)^n log(1+k/n)^(1/n) ,is

The value of lim_(n->oo) sum_(k=1)^n log(1+k/n)^(1/n) ,is

lim_(n->oo)[log_(n-1)(n)log_n(n+1)*log_(n+1)(n+2).....log_(n^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