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))

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 -

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

{:(" "Lt),(n rarr oo):} ((1+2^(4)+3^(4)+......+n^(4))/(n^(5)))-{:(" "Lt),(n rarr oo):} ((1+2^(3)+3^(3)+....+n^(3))/(n^(5)))=

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

Let a = lim_(n rarr oo) (1+2+3+.....+n)/(n^(2))= , b = lim_(n rarr oo) (1^(2)+2^(2)+.....+n^(2))/(n^(3))= then

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))