This course develops sequences and infinite series from basic terms and partial sums through convergence tests, power series, and Taylor and Maclaurin expansions. It also applies series to estimate errors, evaluate limits, and approximate integrals.

Syllabus

Listing the first terms of the sequence (KristaKingMath)
Calculating the first terms of the sequence (KristaKingMath)
Finding a formula for the general term of the sequence (a_n) (KristaKingMath)
Does the sequence converge or diverge? (KristaKingMath)
Finding the limit of a convergent sequence (KristaKingMath)
Increasing, decreasing and not monotonic sequences (KristaKingMath)
Bounded sequences (KristaKingMath)
Calculating the first terms in a series of partial sums (KristaKingMath)
Sum of the series of partial sums (KristaKingMath)
nth term test, divergence test, zero test (KristaKingMath)
Convergence of a geometric series (KristaKingMath)
Convergence and sum of a geometric series, example 1 (KristaKingMath)
Convergence and sum of a geometric series, example 2 (KristaKingMath)
Convergence and sum of a geometric series, example 3 (KristaKingMath)
Values for which the geometric series converges (KristaKingMath)
Repeating decimal expressed as a ratio of integers (KristaKingMath)
Convergence of a telescoping series (KristaKingMath)
Sum of Telescoping Series (KristaKingMath)
p-Series test for convergence (KristaKingMath)
How to use the INTEGRAL TEST for series
Comparison Test (KristaKingMath)
Limit Comparison Test (KristaKingMath)
Estimating error/remainder of a series (KristaKingMath)
Alternating Series Test - Calculus (KristaKingMath)
Alternating series estimation theorem (KristaKingMath)
Ratio Test - Calculus (KristaKingMath)
Ratio Test with Factorials (KristaKingMath)
Root Test - Calculus (KristaKingMath)
Absolute and conditional convergence (KristaKingMath)
Difference Between Limit and Sum of the Series (KristaKingMath)
Radius of convergence (KristaKingMath)
Interval of Convergence (KristaKingMath)
Interval of Convergence Example 2 (KristaKingMath)
Power series representation, radius and interval of convergence (KristaKingMath)
Power series multiplication (KristaKingMath)
Power series division (KristaKingMath)
Power series differentiation (KristaKingMath)
Using power series to estimate a definite integral (KristaKingMath)
Binomial series (KristaKingMath)
Taylor Polynomial Example 1 PART 1/2 (KristaKingMath)
Taylor Polynomial Example 1 PART 2/2 (KristaKingMath)
Taylor Polynomial Example 2 PART 1/2 (KristaKingMath)
Taylor Polynomial Example 2 PART 2/2 (KristaKingMath)
Finding radius of convergence of a Taylor series (KristaKingMath)
Taylor's inequality (KristaKingMath)
Maclaurin Series (KristaKingMath)
Sum of the maclaurin series (KristaKingMath)
Maclaurin series radius of convergence (KristaKingMath)
Expressing the integral as a power series (KristaKingMath)
Using maclaurin series to estimate an indefinite integral (KristaKingMath)
Maclaurin series to estimate a definite integral (KristaKingMath)
Maclaurin series to evaluate a limit (KristaKingMath)