" 25.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)(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 :

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^(n)+3^(n))^(1/n)

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