Use Geometric Series to get Power Series, with Calculus | Derivatives, Integrals

Use derivatives and integrals to transform a function f(x) into the form 1/(1 - [Y]) and therefore can apply the geometric series to write the power series of f(x). Step-by-step examples, and also theory.

0:00 Review using Algebra
2:09 Ex 1. ln(1 + x)
6:59 How to shift index
9:38 Derivative or integral term-by-term
12:28 Ex 2. arctan(x)
16:17 Ex 3. 1/(1 + 2x)^2
23:18 Ex 4. x/(1 - x)^3
29:58 Summary

#Calculus #PowerSeries #GeometricSeries #MathMadeEasy #CalculusShortcuts #LearnMath #APCalc #apcalculusbc

Видео Use Geometric Series to get Power Series, with Calculus | Derivatives, Integrals канала Vu Do Math