evaluate `lim_(n->oo)((e^n)/pi)^(1/ n)`

Evaluate: (lim)_(n->oo)[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

The value of lim_(nto oo)(a^(n)+b^(n))/(a^(n)-b^(n)), (where agtbgt1 is

The value of lim(n->oo)((1.5)^n + [(1 + 0.0001)^(10000)]^n)^(1/n) , where [.] denotes the greatest integer function is:

The value of lim_(n -> oo)(1.n+2.(n-1)+3.(n-2)+...+n.1)/(1^2+2^2+...+n^2)

Let S_(n),n=1,2,3,"…" be the sum of infinite geometric series, whose first term is n and the common ratio is (1)/(n+1) . Evaluate lim_(n to oo)(S_(1)S_(n)+S_(2)S_(n-1)+S_(3)S_(n-2)+"..."+S_(n)S_(1))/(S_(1)^(2)+S_(2)^(2)+"......"+S_(n)^(2)) .

The value of the lim_(n->oo)tan{sum_(r=1)^ntan^(- 1)(1/(2r^2))} is equal to

Definite integration as the limit of a sum : lim_(ntooo)[(n!)/(n^(n))]^(1/n)=.........

The value of lim_(n->oo)sum_(k=1)^n(6^k)/((3^k-2^k)(3^(k+1)-2^(k+1)) is equal to

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

The value of lim_(nto oo)(1^(3)+2^(3)+3^(3)+……..+n^(3))/((n^(2)+1)^(2))