Limit comparison help

[Moistwh]

I need to use the limit comparison test to determine if converges or diverges

Do i need to compare it to n^2/2^n?

 

[MarkFL]

I'm thinking I would try:

[MATH]b_n=3^n[/MATH]
since:

[MATH]\frac{a_n}{b_n}=\frac{\dfrac{6^n+n^2}{2^n+\ln(n)}}{3^n}=\frac{6^n+n^2}{6^n+3^n\ln(n)}[/MATH]
So, what is:

[MATH]\lim_{n\to\infty}\left(\frac{6^n+n^2}{6^n+3^n\ln(n)}\right)[/MATH] ?

 

[Moistwh]

The limit is 1, meaning that the series is divergent, since 3^n is a divergent series with r > 1

Thank you

 

[MarkFL]

The limit is 1, meaning that the series is divergent, since 3^n is a divergent series with r > 1

Thank you

Yes, exactly!