Ratio Test for Infinite Series Example with SUM(n^5/3^n) | Summary and Q&A

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June 30, 2020
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The Math Sorcerer
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Ratio Test for Infinite Series Example with SUM(n^5/3^n)

TL;DR

Learn how to determine convergence or divergence of an infinite series using the ratio test.

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Key Insights

  • 🥳 The ratio test is a useful tool for determining the convergence or divergence of an infinite series.
  • 🥳 By substituting n with n+1 and simplifying, the ratio of consecutive terms can be evaluated.
  • 🥳 If the limit of the ratio is less than 1, the series converges; if it is greater than 1, the series diverges; if it is equal to 1, no information is obtained.

Transcript

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Questions & Answers

Q: What is the ratio test used for?

The ratio test is used to determine if an infinite series converges or diverges by analyzing the limit of the ratio of consecutive terms.

Q: How is the ratio test applied?

To apply the ratio test, substitute n with n+1 in the series and simplify, then evaluate the limit as n tends to infinity.

Q: What does it mean if the limit in the ratio test is less than 1?

If the limit of the ratio of consecutive terms is less than 1, the series converges.

Q: What happens if the limit in the ratio test is greater than 1?

If the limit of the ratio of consecutive terms is greater than 1, the series diverges.

Summary & Key Takeaways

  • The ratio test is used to determine if an infinite series converges or diverges based on the limit of the ratio of consecutive terms.

  • By substituting n with n+1 in the series and simplifying, the limit can be evaluated.

  • If the limit is less than 1, the series converges. If it is greater than 1, the series diverges. If it is equal to 1, no information is obtained.

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