Problem

Determine whether the series is convergent or div…

05:31

Problem 11 Easy Difficulty

Determine whether the series is convergent or divergent.
$ 1 + \frac {1}{8} + \frac {1}{27} + \frac {1}{64} + \frac {1}{125} + \cdot \cdot \cdot $

Answer

converges by (1).

Discussion

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Video Transcript

in this problem, we have to determine if a Siri's is convergent or divergent. So the Siri's that were given isn't really in the form of a normal, normal Siri's with the Sigma. But we have to get it in that form to determine if it's convergent or not. So we're given this Siri's one plus 1/8 plus 1/27 plus 1/64 plus one over 125. Now, if we look at this, Siri's closely, we can see that we have a pattern here. So this is the same thing is saying that we have the some from n equals one to infinity of one over and cubed, so that looks like a form that we can test the convergence off. This is a part of me. This is a P Siri's, and in this case, P equals three and three is clearly greater than one. So that means that this Siri's is convergent by the P Siri's test. I hope that this problem help you understand a little bit more about Siri's, specifically how we can tell if a syriza's converging or not using the P Siri's test

Madi S.

University of Denver

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 3

The Integral Test and Estimates of Sums

Problem