The Integral Test The integral test compares a series to its integral to prove convergence or divergence! This test is best illustrated by examples, so let’s look at some of them together. Examples Worked Solutions Solution to a) NOTE: I forgot the dn in the first two integrals, don’t make my mistake! We can apply […]
AP Calc 10.4 Integral Test for Convergence Read More »
Learn all about the definition of p-series, harmonic series, and how to determine their convergence or divergence with this AP Calculus 10.5 study guide!
AP Calc 10.5 Harmonic Series and P-Series Read More »
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
AP Calc 10.3 The nth Term Test for Divergence Read More »
AP Calculus Unit 10 study guides, worked examples, practice problems, and amazing resources for mastery of sequences and series!
AP Calc BC Unit 10 Read More »
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
AP Calc 10.9 Absolute or Conditional Convergence Read More »
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
AP Calc 10.8 Ratio Test for Convergence Read More »
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
AP Calc 10.7 Alternating Series Test for Convergence Read More »
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
AP Calc 10.6 Comparison Tests for Divergence Read More »
Discover the foundational concepts of sequences and their convergence in this AP Calculus BC Unit 10.1 study guide. From arithmetic and geometric sequences to the divergence and convergence of series, master essential topics with clear explanations and practice exercises.
AP Calc 10.1 Defining Convergent and Divergent Infinite Series Read More »
Easy-to-understand study guide for AP Calc 10.2 Working with Geometric Series! Quick summary of key content and practice questions.
AP Calc 10.2 Working with Geometric Series Read More »
