Lessons

AP Calc 10.3 The nth Term Test for Divergence

Nth Term Test for Divergence The nth term test tests for divergence with the following condition: However, it only tests for divergence. It cannot prove convergence. Therefore,  Choose another test if this happens. This happens because if the terms don’t approach 0, the series will continue growing and growing (diverging).  Examples Worked Solutions Solution to a) A more

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AP Calc 10.9 Absolute or Conditional Convergence

Absolute or Conditional Convergence Examples Worked Solutions Solution a) Solution b) Solution c) More Resources Flipped Math Flipped Math is an awesome resource with full packets, test prep, and corrective assignments for each lesson! Flipped Math Lesson 10.9 Math Libretexts Math LibreTexts is a free online resource packed with textbooks and learning materials for math

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AP Calc 10.8 Ratio Test for Convergence

Ratio Test for Convergence The Ratio Test tests for absolute convergence. It is particularly useful for complicated-looking series with factorials or exponentials. Let’s dive in with the definition:  Recall: Examples Hint: b) is a challenge problem requiring knowledge about the limit definition of e.  Worked Solutions Solution a) Solution b) Solution c) More Resources Flipped

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AP Calc 10.7 Alternating Series Test for Convergence

Alternating Series Test The mathy definition for the alternating series test is as follows:  In other words, an alternating series converges if it’s terms alternate in sign, have a limit of 0, and get smaller and smaller (decrease in magnitude). The Alternating Series Test only proves convergence. If a test fails one of the requirements, it doesn’t mean

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AP Calc 10.6 Comparison Tests for Divergence

AP Calc 10.6 Comparison Tests for Divergence Note: I’ll be using an and bn to denote each series since I can’t do subscripts.  Direct Comparison Test The comparison test is a method to determine whether a series converges or diverges. The definition of the test is as follows:  In other words: If you have a convergent

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