The videos in this application cover sequences and series. This means that we'll cover basics like series vs sequences, convergent series, telescoping series, telescoping series, using partial sums to show series divergence, and geometric series. Additionally, we'll look at more advanced applications and concepts like integral tests for series, remainder estimates for the integral test, limit tests, direct comparison tests, alternating series, ratio tests, absolute convergence, power series, Maclaurin series, Taylor series, using series to evaluate limits and approximate integrals, and the binomial series. To learn about these concepts, we'll cover the topic through a series of video lessons, each of which will cover pertinent ideas and related problems. The video content in this application will include a lesson on each of the following:* What is a Sequence? Basic Sequence Info* More Convergent Sequence Examples* What is a Series?* Telescoping Series* Using Partial Sums to Show a Series Diverges* Geometric Series, Pt 1* Geometric Series, Pt 2* Geometric Series: More Examples* Geometric Series: Repeating Decimal as Fraction* Integral Test for Series* Remainder Estimate for the Integral Test* Limit and Direct Comparison Tests, Pt 1* Limit and Direct Comparison Tests, Pt 2* Alternating Series* Alternating Series: Another Example* Alternating Series: Estimation Theorem* Ratio Test and Absolute Convergence, Pt 1* Ratio Test and Absolute Convergence, Pt 2* Strategy for Testing Series: Overview* Power Series: Finding the Interval of Convergence* Power Series Representations: PSR for 1/(1 - x)* Power Series: Multiplying and Dividing* Differentiating and Integrating Power Series* Find a Maclaurin Series* Finding a Taylor Series Expansion* Taylor's Inequality* Using Series to Evaluate Limits* Maclaurin/Taylor to Approximate Definite Integrals* The Binomial Series, Ex 1* The Binomial Series, Ex 2This is one of several Calculus apps from me, PatrickJMT. I have been putting up math videos for a few years on YouTube and now have the most popular 'math only' channel on YouTube!, Affter much encouragement and many requests from my YouTube friends, I've finally decided to organize the videos and put them out as an App. I've been teaching math for >8 years at the college/university level and tutoring for over 20 years. In the past, I have taught at Vanderbilt University (a top 20 ranked university), the University of Louisville and at Austin Community College.
