- #1
waealu
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Homework Statement
Does the following series converge or diverge (use either the Limit Comparison or the Direct Comparison Test):
[tex]\sum_{n=1}^{+\infty} \frac{3^{n-1}+1}{3^{n}}[/tex]
Homework Equations
In a previous problem that was
[tex]\sum_{n=1}^{+\infty} \frac{1}{3^{n-1}+1}[/tex]
I was able to reindex the series to make it
[tex]\sum_{n=0}^{+\infty} \frac{1}{3^{n}+1}[/tex]
From there, I took 1/(3n+1)<1/3n.
Therefore, since 1/3n converges, [tex]\sum_{n=1}^{+\infty} a_{n}[/tex] also converges.
The Attempt at a Solution
However, I don't know how to solve the series that I'm currently on.
Thanks,
Erik