`lim_(ntoinfty) (n/(n^2+1^2)+n/(n^2+2^2)+n/(n^2+3^2)+...+n/5n^2)` is equal to

lim_(n to oo ) {(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+ (n)/(n^(2)+n^(2))} is equal to

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

lim_(n rarr oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2)) + (n)/(n^(2)+3^(2))+......+(1)/(5n)) is equal to :

The value of lim_(n rarr infty) (1)/(n) {(n+1)(n+2)(n+3)…(n+n)}^(1//n) is equal to

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 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

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

lim_(n rarr infty) sum_(k=1)^(n) (n)/(n^(2)+k^(2)x^(2)),x gt 0 is equal to

lim_(nto oo) {(1)/(n+1)+(1)/(n+2)+(1)/(n+3)+...+(1)/(n+n)} is, equal to

Let alpha=lim_(n->oo)((1^3-1^2)+(2^3-2^2)+.....+(n^3-n^2))/(n^4), then alpha is equal to :