`underset(n to oo)lim{(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+ (n)/(n^(2)+n^(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 to oo)[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+....+(1)/(n)]

underset(n to oo)lim ((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1))

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

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

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 :

underset(n to oo)lim {1/(1-n^(2))+(2)/(1-n^(2))+....+(n)/(1-n^(2))} is equal to

lim _(n to oo) ( 1/(n^(2)+1^(2)) + 1/(n^(2)+2^(2)) +...1/(2n^(2))) equals

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