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Infinite Series Convergence Tests worksheets

Choose and justify nth-term, geometric, p-series, ratio, direct-comparison, and limit-comparison tests.

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Name a valid convergence test, apply it with enough exact work, and state whether the series converges or diverges.

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Learning objective

What this activity builds

Select a valid convergence test and connect its exact limit or inequality to a conclusion.

Worked example

Does sum 3^n/n! converge?

Yes. The ratio is 3/(n+1), whose limit is 0<1.

The ratio test gives absolute convergence.

Teaching notes

Make the practice count

  • Check the nth-term condition before stronger tests.
  • State the comparison series and why it is known.
  • Write the decisive limit or ratio, not only the test name.

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Math SheetNameScoreTeacherDateInfinite Series Convergence TestsName a valid convergence test, apply it with enough exact work, and state whether the series converges or diverges.1.Determine convergence of sum from n=1 to infinity of n!/4^n. Name and apply a valid test.2.Determine convergence of sum from n=1 to infinity of n/(n+1). Name and apply a valid test.Show your reasoning. Keep exact values unless instructed otherwise.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateInfinite Series Convergence TestsName a valid convergence test, apply it with enough exact work, and state whether the series converges or diverges.3.Determine convergence of sum from n=1 to infinity of 1/(n^2+1). Name and apply a valid test.4.Determine convergence of sum from n=1 to infinity of 1/n^2. Name and apply a valid test.Show your reasoning. Keep exact values unless instructed otherwise.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateInfinite Series Convergence TestsName a valid convergence test, apply it with enough exact work, and state whether the series converges or diverges.5.Determine convergence of sum from n=1 to infinity of 3^n/n!. Name and apply a valid test.6.Determine convergence of sum from n=1 to infinity of 1/(n+1). Name and apply a valid test.Show your reasoning. Keep exact values unless instructed otherwise.math-sheet.comPage 3 of 3

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