(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant 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/(3^{n}+1)<1/3^{n}.

Therefore, since 1/3^{n}converges, [tex]\sum_{n=1}^{+\infty} a_{n}[/tex] also converges.

3. The attempt at a solution

However, I don't know how to solve the series that I'm currently on.

Thanks,

Erik

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# Homework Help: Comparison Tests for Series

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