Evaluate `underset(ntooo)limn^(-n^(2))[(n+2^(0))(n+2^(-1))(n+2^(-2))...(n+2^(-n+1))]^(n)`.

Evaluate lim_(ntooo) n^(-n^(2))[(n+2^(0))(n+2^(-1))(n+2^(-2))...(n+2^(-n+1))]^(n) .

Evaluate lim_(ntooo) (1)/(1+n^(2))+(2)/(2+n^(2))+...+(n)/(n+n^(2)).

lim_(n to oo)[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+....+(1)/(n)]

underset(nrarroo)lim[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+(n+3)/(n^(2)+3^(2))+...+(1)/(n)]

Evaluate the following (i) lim_(n to oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))....+(n-1)/(n^(2))) (ii) lim_(n to oo)((1)/(n+1)+(1)/(n+2)+....+(1)/(2n)) (iii) lim_(n to oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+(n)/(2n^(2))) (iv) lim_(n to oo)((1^(p)+2^(p)+.....+n^(p)))/(n^(p+1)),pgt0

Evaluate lim_(ntooo) nsin(2pisqrt(1+n^(2))),(n inN).

Evaluate lim_(ntooo) (n^(p)sin^(2)(n!))/(n+1),"wher "0ltplt1.

The value of lim_(n to oo)[(n)/(n^(2))+(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+...+(n)/(n^(2)+(n-1)^(2))] is :

Evaluate lim_(ntooo) ((1^(2)-2^(2)+3^(2)-4^(2)+5^(2)+...n" terms"))/(n^(2)).

lim_(ntooo) ((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1)) is equal to