Step-by-step math courses covering Pre-Algebra through Calculus 3.
 

Master Sequences & Series

Learn everything from Sequences & Series, then test your knowledge with 310+ practice questions

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Sequences & Series Testimonial

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Excellent! I have already learned so much and LOVE the teaching style.
 
 
Sequences & Series course summary

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Course Summary

Learn everything you need to know to get through Sequences & Series and prepare you to go into Calculus 3 with a solid understanding of what’s going on. Video explanations, text notes, and quiz questions that won’t affect your class grade help you “get it” in a way most textbooks never explain.

 
 
Sequences & Series course outline

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Course outline

The curriculum includes:

  • Introduction to sequences

    • Sequences vs. series

    • Listing the first terms

    • Calculating the first terms

    • Formula for the general term

    • Convergence of a sequence

    • Limit of a convergent sequence

    • Increasing, decreasing, and not monotonic

    • Bounded sequences

  • Partial sums

    • Calculating the first terms of a series of partial sums

    • Sum of the series of partial sums

  • Geometric series

    • Geometric series test

    • Sum of the series

    • Values for which the series converges

    • Repeating decimals

  • Telescoping series

    • Convergence

    • Sum of the series

  • Basic convergence tests

    • Recognizing types of series

    • Limit vs. sum of the series

    • Integral test

    • p-series test

    • nth term test (aka divergence test, zero test)

  • Comparison tests

    • Comparison test

    • Limit comparison test

    • Error of a series (remainder of a series)

  • Ratio and root tests

    • Ratio test

    • Ratio test with factorials

    • Root test

    • Absolute and conditional convergence

  • Alternating series test

    • Alternating series test

    • Alternating series estimation theorem

  • Power series

    • Power series representation

    • Power series multiplication and division

    • Power series differentiation

    • Radius of convergence, interval of convergence

    • Estimating definite integrals, estimating indefinite integrals

    • Binomial series

  • Taylor series

    • Taylor series

    • Radius of a Taylor series, interval of convergence of a Taylor series

    • Taylor's inequality

  • Maclaurin series

    • Maclaurin series

    • Sum of a Maclaurin series

    • Radius of a Maclaurin series, interval of convergence of a Maclaurin series

    • Evaluating indefinite integrals as an infinite series

    • Estimating indefinite integrals

    • Estimating definite integrals

    • Evaluating limits

 
 
Subscribe to the Sequences & Series course

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Ready to Master Sequences & Series?

 
Sequences & Series course
 

 

By signing up for the Sequences & Series course, you'll gain access to:

  • Step-by-step videos

  • Course notes and flashcards

  • Practice quizzes

  • Bonus practice workbooks

  • Comprehensive formula sheets

  • Summary study sheets

  • Practice final exams

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Just $39 per month, and you can cancel easily from your dashboard at any time.