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In this article, we will again consider infinite series and how to check for convergence. Therefore, we will look closer at the Ratio Test. If you need, you can read up on infinite series and how to check for convergence in the following articles: Infinite Series, Special Series, and Integral Test.
Introducing the Ratio Test
Let us first introduce how the ratio test is performed. Imagine that we have the series:
We can then define the following:
Then, we have the following:
Example of the Ratio Test
Let us then try to take an example. Imagine that we have the following series:
We can then also say that we have:
We can then calculate L, which gives us:
We can see that we have:
We can then see that L < 1, hence our series is absolutely convergent.
Conclusion
We have now seen what the ratio test is, and how it works to determine whether a series is convergent or divergent.
References
- Dawkins, P. (2003). Section 4–4 : Convergence/Divergence Of Series. Pauls Online Math Notes. https://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx
- Dawkins, P. (2003). Section 4–3 : Series — The Basics. Pauls Online Math Notes. https://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx
- Dawkins, P. (2003). Section 4–10 : Ratio Test. Pauls Online Math Notes. https://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx
