`lim _( n to oo) (1+2^(4) + 3 ^(4) + ..... + n ^(4))/(n ^(5)) - lim _(n to oo) (1+ 2 ^(2) + 3^(3) + ..... + n ^(3))/(n ^(5)) ` is:

lim_(n to oo){(1^(m)+2^(m)+3^(m)+...+ n^(m))/(n^(m+1))} equals

lim_(n rarr oo)2^(1/n)

lim_(n to oo)(1-2n^(2))/(5n^(2)-n+100)=

lim_(n->oo)(1^(99)+2^(99)+3^(99)+.......n^(99))/(n^(100))=

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

Evaluate lim _( x to oo) ((1^(2) )/(n ^(3) +1 ^(3))+(2 ^(2))/(n ^(3) +2 ^(3)) + (3 ^(2))/(n ^(3)+ 3 ^(3))+ .... + (4)/(9n)).

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

lim_(nto oo) (2^n+5^n)^(1//n) is equal to

lim_(n to oo)(n!)/((n+1)!-n!)