Series videos

Convergent and divergent sequences

Worked example: sequence convergence/divergence

Partial sums intro

Partial sums: term value from partial sum

Partial sums: formula for nth term from partial sum

Infinite series as limit of partial sums

Worked example: divergent geometric series

Worked example: convergent geometric series

Infinite geometric series word problem: bouncing ball

Infinite geometric series word problem: repeating decimal

Convergent & divergent geometric series (with manipulation)

nth term divergence test

Integral test

Worked example: Integral test

Harmonic series and 𝑝-series

Worked example: p-series

Worked example: direct comparison test

Direct comparison test

Limit comparison test

Worked example: limit comparison test

Proof: harmonic series diverges

Alternating series test

Worked example: alternating series

Ratio test

Conditional & absolute convergence

Alternating series remainder

Worked example: alternating series remainder

Taylor & Maclaurin polynomials intro (part 1)

Taylor & Maclaurin polynomials intro (part 2)

Worked example: coefficient in Maclaurin polynomial

Worked example: Maclaurin polynomial

Visualizing Taylor polynomial approximations

Worked example: coefficient in Taylor polynomial

Taylor polynomial remainder (part 1)

Taylor polynomial remainder (part 2)

Worked example: estimating sin(0.4) using Lagrange error bound

Worked example: estimating eˣ using Lagrange error bound

Power series intro

Worked example: interval of convergence

Function as a geometric series

Power series of arctan(2x)

Power series of ln(1+x³)

Geometric series as a function

Geometric series interval of convergence

Maclaurin series of cos(x)

Maclaurin series of sin(x)

Worked example: power series from cos(x)

Maclaurin series of eˣ

Visualizing Taylor series approximations

Worked example: cosine function from power series

Worked example: recognizing function from Taylor series

Euler's formula & Euler's identity

Integrating power series

Finding function from power series by integrating

Differentiating power series

Interval of convergence for derivative and integral

Converting explicit series terms to summation notation

Converting explicit series terms to summation notation (n ≥ 2)

Divergent telescoping series

Telescoping series

Formal definition for limit of a sequence

Proving a sequence converges using the formal definition

Finite geometric series formula

Proof of infinite geometric series as a limit

Infinite geometric series formula intuition

Proof of p-series convergence criteria