`lim_(n->oo) (1)/(n^(6)){(n+1)^(5)+(n+2)^(5)+...+(2n)^(5)}`

lim _(nrarroo)(1)/(n^(6)){(n+1)^(5)+(n+2)^(5)+...+(2n)^(5)}

lim_(n rarr oo)(5^((1)/(n))+3^(1/n)-1)^(n)

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

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

lim_(n rarr oo)((1^(4))/(1^(5)+n^(5))+(2^(4))/(2^(5)+n^(5))+(3^(4))/(3^(5)+n^(5))+--+(n^(4))/(n^(5)+n^(5)))

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

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

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 rarr oo) (4^(n)+5^(n))^(1/n) =