Evaluate : `lim_(n-> oo) (1^4+2^4+3^4+...+n^4)/n^5 - lim_(n->oo) (1^3+2^3+...+n^3)/n^5`

Evaluate: lim_(n->oo)(4^n+5^n)^(1/n)

The value of lim_(n rarr oo) (1 + 2^(4) + 3^(4) +…...+n^(4))/(n^(5)) - lim_(n rarr oo) (1 + 2^(3) + 3^(3) +…...+n^(3))/(n^(5)) is :

lim_(n->oo) [ (1^3+ 2^3 + 3^3 -------n^3)/n^4]

The value of [lim_(n to oo)(1+2^(4)+3^(4)+...+n^(4))/(n^(5))-lim_(n to oo)(1+2^(3)+3^(3)+...+n^(3))/(n^(5))] is equal to -

Evaluate: ("lim")_(n->oo)(4^n+5^n)^(1/n)

lim_(n->oo) (1.2+2.3+3.4+....+n(n+1))/n^3

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

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