Question

Determine whether the series converges or diverges.
n + 6/( n^10 + n^3)^(1/3)

Answer 1

\[\sum_{n=1}^{\infty}\frac{n+6}{(n^{10}+n^3)^{1/3}}\]
yes?

Answer 2

yes

Answer 3

I think it will have to converge, but I'm having trouble honestly... I don't remember all the ways to show convergence... but the top is getting closer to inf much slower than the bottom (despite the cube root)... which means that you will essentially have n/inf and converge.

Answer 4

i found it, thanks

Answer 5

1 - (2 n^2 (3 + 10 n^7))/(n^3 + n^10)^(4/3)