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

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

summation [cos((n)pi)/3] / n!

from 1 to inf

2. Relevant equations

convergence tests

3. The attempt at a solution

I tried using the ratio test but that was ineffective since I ended up with cos(inf) in the numerator and denominator.

So then I tried using squeeze theorem.

I did -1/n! <eq a_n <eq 1/n!

Seeing as how -1/n! and 1/n eventually reach 0, I concluded that a_n is absolutely convergent.

Other than this, I have 2 other general questions:

1. Does cos(inf) exist?

2. Is it valid to use squeeze theorem for series?? (I've only effectively used them for sequences)

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# Homework Help: Absolute convergence?

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