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Numerade Educator

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Problem 25 Easy Difficulty

Determine whether the series is convergent or divergent.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {1}{n^2 + n^3} $

Answer

convergent

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Video Transcript

for this problem. We will use the comparison test if we rewrite the Siri's as and equals. Want insanity of one over and the square Times quality one plus m, and we realized that one plus n So it's going to be greater than pick one. This means that one over and squared times one plus end. We'LL have a larger denominator, then just one over and squared. In other words, we have this inequality one over and square times one plus and is less than one over just n squared. You know, we know that this converges, but peace Siri's. So we have our original Siri's always less than or equal to some conversion. Siri's. Therefore, Siri's is inversion itself.