Question

Test for convergence:

(n+5)/((n^7+n^2)^(1/3)) from 1 to inf.

I cannot figure out which test to use. any help would be great!

Answer 1

you know that 1/n^p converges for p>1.

Loosely,
(n+5)/((n^7+n^2)^(1/3))
< (n+5)/n^(7/3)
< (n+5)/n^2.33
< 1/n^1.33
so it converges