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

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

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 :

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))

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))

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

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

lim_(n rarr oo)(2^(3n))/(3^(2n))=