.01

.02

.03

• 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

.04

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

We’ve got this. 👊