Test for Divergence (infinite series)

TL;DR

The test for divergence involves taking the limit to determine if a series diverges; zero indicates convergence.

Transcript

okay another question on my final exam this time in the multiple choice format we wanted to know which of the series right here diverges by test for divergence so of course what to know what does the test for divergence dead so let me just write this down for you guys all we have to do is to take the limit so today if you see the limit of n goes to... Read More

Key Insights

• 🤪 The test for divergence involves taking the limit of a series as n goes to infinity to determine convergence or divergence.
• ⛔ If the limit of the series is not zero, then the series diverges.
• 🏆 The starting value of n does not affect the outcome of the test for divergence.
• 🏆 Further analysis may be needed if the limit in the test for divergence is zero to determine convergence or divergence accurately.

Questions & Answers

Q: What does the test for divergence involve?

The test for divergence involves taking the limit of a series to determine if it converges or diverges. If the limit is not zero, the series diverges.

Q: How does the starting value of n impact the test for divergence?

The starting value of n does not impact the test for divergence; only the limit of the series as n approaches infinity matters in determining convergence or divergence.

Q: What happens if the limit in the test for divergence is zero?

If the limit in the test for divergence is zero, the series may converge or diverge, and further testing or analysis is required for a conclusive answer.

Q: How can the test for divergence be applied to different series?

The test for divergence can be applied to various series to determine their convergence or divergence based on the limit of the series as n approaches infinity.

Summary & Key Takeaways

• The test for divergence involves taking the limit of a series to see if it converges or diverges based on the result.

• If the limit is not zero, then the series diverges as n goes from 1 to infinity.

• The starting value of n does not affect the outcome of the test for divergence.