What is the sum of Does it converge or diverge Show all of y

What is the sum of:

Does it converge or diverge? Show all of your work.

Solution

our break point is at x=inf
we know if f(x)/g(x)=l and if l is nonzero finite, f(x) and g(x) have same nature of convergence or divergence.
let g(x)=sqrt(n)

at n=inf, f(x)/g(x)=1

and g(x)=divergent in same limits

hence f(x) is also divergent

:)