nth Term Test, Divergence, Infinite Series, Examples - Calculus

The nth term test for divergence is a simple test that states if the limit of a series' terms as \(n\) approaches infinity is not equal to zero, then the series diverges. If the limit is zero, the test is inconclusive, and another test must be used to determine if the series converges or diverges. This test is useful for quickly identifying divergent series but cannot be used to prove convergence.

💡How to apply the nth term test for divergence
• Identify the general term: (\(a_{n}\)) of the series.
• Find the limit: of \(a_{n}\) as \(n\) approaches infinity ($ \lim_{n \to \infty} a_n $).
• Draw a conclusion:
◦ If the limit is not zero ($ \lim_{n \to \infty} a_n \neq 0 $), then the series diverges.
◦ If the limit is zero ($ \lim_{n \to \infty} a_n = 0 $), then the test is inconclusive and other tests must be used

💡Worksheets are provided in PDF format to further improve your understanding:
• Questions Worksheet: https://drive.google.com/file/d/1DlYi7xcmyEAhWTnwUN8zRgisBdHIdmtr/view?usp=drive_link
• Answers: https://drive.google.com/file/d/1VEHFVDs67vvvQVVsozjmOCO5RbEgzbkA/view?usp=drive_link

💡Chapters:
00:00 nth term test for divergence
01:00 Worked examples

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