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Numerade Educator



Problem 4 Easy Difficulty

Determine whether the series is absolutely convergent or conditionally convergent.

$ \displaystyle \sum_{n = 1}^{\infty} \frac {( - 1)^n}{n^3 + 1} $


Absolutely Convergent


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Video Transcript

let's go ahead and show that the series will be absolute conversion. Sure. So here we should look at this. Siri's obtained by taking the absolute value. Now the sequels, however, this is less than or equals who one over and tube. Why is this true? Therefore, that's true. And the Siri's convergence bye pee test with P equals three, which is bigger than one. That's the Peter the exponents. So by the comparison test absolute value here, the Siri's of absolute values conversions now. Therefore, we've just shown that the Siri's is absolutely commercial, and that's our finalists.