Introduction to series
An infinite series can be thought of as an attempt to add up an infinite collection of numbers. In this video we define the sequence of partial sums associated to an infinite series, as well as the notions of convergence and divergence for a series. The convergence of the geometric series 1 + 1/2 + 1/4 + 1/8 + ... is demonstrated using areas of rectangles. The series 1 - 1 + 1 - 1 + ... is used to motivate a discussion of why infinite series are such subtle creatures.
Видео Introduction to series канала Chris Odden
Видео Introduction to series канала Chris Odden
Показать
Комментарии отсутствуют
Информация о видео
Другие видео канала
![Velocity, speed, and acceleration](https://i.ytimg.com/vi/_YC1C-kLMUI/default.jpg)
![Improper integrals: decomposing compound improper integrals into a sum of simple improper integrals](https://i.ytimg.com/vi/OokGm_Ndp7E/default.jpg)
![Rates of change, net change, and signed areas under graphs](https://i.ytimg.com/vi/_-VaFGlnbE8/default.jpg)
![The alternating harmonic series](https://i.ytimg.com/vi/82NXcfmAKZM/default.jpg)
![Polynomial approximations of functions (Introduction to the Taylor recipe)](https://i.ytimg.com/vi/3EHeG279h24/default.jpg)
![The general geometric series a+ax+ax^2+...](https://i.ytimg.com/vi/cT2S8nUvd4A/default.jpg)
![Derivatives of scalar multiples, sums, and differences of functions](https://i.ytimg.com/vi/vIrOpmgpH_g/default.jpg)
![A test for monotonicity: Using the derivative to understand the monotonicity of a function](https://i.ytimg.com/vi/fiCwhsk3PVM/default.jpg)
![Cylindrical shells and the volume of a solid of revolution](https://i.ytimg.com/vi/ZebMFhuxfd0/default.jpg)
![The "1-4-1" rule](https://i.ytimg.com/vi/Igh9Epomi1g/default.jpg)
![Simple harmonic motion](https://i.ytimg.com/vi/_iNwD9E9ZIs/default.jpg)
![QuickVid: Analyzing relative extrema](https://i.ytimg.com/vi/30LgsqG0llg/default.jpg)
![The derivative of an exponential function](https://i.ytimg.com/vi/bsbipiiq0fc/default.jpg)
![Monotonicity (What it means for a function to be increasing or decreasing)](https://i.ytimg.com/vi/Ca7JC4Of8IA/default.jpg)
![Tangent slopes of polar curves](https://i.ytimg.com/vi/a1-dDub1sOk/default.jpg)
![Improper integrals: integration on a semi-infinite interval](https://i.ytimg.com/vi/1Tsa6pBvJDQ/default.jpg)
![Regular Riemann sums: left-hand sums, right-hand sums, and midpoint sums](https://i.ytimg.com/vi/35Hxspsho0E/default.jpg)
![Optimization](https://i.ytimg.com/vi/c_ERLbtvZLc/default.jpg)
![Introduction to limits](https://i.ytimg.com/vi/c4yJhhGwwzA/default.jpg)
![The Basel Problem: finding the sum of the reciprocals of the squares](https://i.ytimg.com/vi/IBRWHY0VSLQ/default.jpg)