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JH
Numerade Educator

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Problem 27 Easy Difficulty

Determine whether the series is convergent or divergent. If it is convergent, find its sum.
$ \frac {1}{3} + \frac {1}{6} + \frac {1}{9} + \frac {1}{12} + \frac {1}{15} + \cdot \cdot \cdot $

Answer

Diverges

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Video Transcript

let's determine whether the Siri's is conversion or diversion, and if it is, conversion will go ahead and find some as well. So this Siri's, we can go ahead. And if it did converse, we should just be able to pull out of one over three and rewrite. This is and so on. However, the Siri's and the inside of the parentheses. We can rewrite this as the sum and equals one to infinity of one over end. If you want, you could think of this. One is one over one. But as mentioned in your textbook, this is a well known example. Call the harmonic series, and this one actually diverges. And if you take a diversion, Siri's and if you multiply it by one over three, it'LL still that verge. Though this whole thing here diverges, and therefore this sum that was given to us will also die average. So that version, and that's our final answer