EE-Learning
Proving a sequence converges using the formal definition
Catogry:
Math
Subject:
AP Calculus BC
Course:
Infinite Sequences And Series
Lecture List
Proof of p-series convergence criteria
Proof of infinite geometric series as a limit
Infinite geometric series formula intuition
Finite geometric series formula justification
Proving a sequence converges using the formal definition
Formal definition for limit of a sequence
Interval of convergence for derivative and integral
Finding function from power series by integrating
Differentiating power series
Integrating power series
Geometric series interval of convergence
Euler's formula & Euler's identity
Visualizing Taylor series approximations
Worked example: recognizing function from Taylor series
Worked example: cosine function from power series
Worked example: power series from cos(x)
Maclaurin series of eˣ
Maclaurin series of sin(x)
Maclaurin series of cos(x)
Power series of ln(1+x³)
Power series of arctan(2x)
Geometric series as a function
Function as a geometric series
Worked example: interval of convergence
Power series intro
Worked example: estimating eˣ using Lagrange error bound
Worked example: estimating sin(0.4) using Lagrange error bound
Taylor polynomial remainder (part 2)
Taylor polynomial remainder (part 1)
Visualizing Taylor polynomial approximations
Worked example: coefficient in Taylor polynomial
Worked example: coefficient in Maclaurin polynomial
Worked example: Maclaurin polynomial
Taylor & Maclaurin polynomials intro (part 2)
Taylor & Maclaurin polynomials intro (part 1)
Worked example: alternating series remainder
Alternating series remainder
Conditional & absolute convergence
Ratio test
Worked example: alternating series
Alternating series test
Proof: harmonic series diverges
Worked example: limit comparison test
Limit comparison test
Worked example: direct comparison test
Direct comparison test
Worked example: p-series
Worked example: Integral test
Integral test
nth term divergence test
Infinite geometric series word problem: repeating decimal
Infinite geometric series word problem: bouncing ball
Worked example: divergent geometric series
Worked example: convergent geometric series
Infinite series as limit of partial sums
Partial sums: term value from partial sum
Partial sums: formula for nth term from partial sum
Partial sums intro
Worked example: sequence convergence/divergence
Convergent and divergent sequences