Discrete Math II/Combinatorics (Entire course) - Discrete Math II - 8.4.7 Solve Recurrence Relations with Generating Functions

We will utilize everything we have learned in the previous 6 videos to learn how to solve recurrence relations using generating functions. This is a longer video, but there is a LOT of prior knowledge you will be tapping into. We take our time through one example involving partial fractions and solving a system of 3 equations. We end with creating the generating function from a recurrence relation that we previously solved for explicitly. Video Chapters: Intro 0:00 Helpful Table 0:15 Creating Equations from Your Recurrence Relation 0:24 Creating Summations from Addition of Recurrence Relations 1:26 Substituting the Power Series G(x) 4:13 The Generating Function G(x) 8:44 Write the Closed-Form Expression of the Generating Function 12:47 Solve a System of 3 Equations 17:09 Create the Explicit Function from the Generating Function 22:00 Checking Your Work 24:16 Practice for Creating a Closed-Form GenFun from Recur.Rel 25:01 Up Next 34:32 This playlist uses Discrete Mathematics and Its Applications, Rosen 8e Power Point slide decks to accompany the videos can be found here: https://bellevueuniversity-my.sharepoint.com/:f:/g/personal/kbrehm_bellevue_edu/Ei9DcmrOBTlAuMxWUoq9ZqsB14M60jcpob-xdAYS6ruVWw?e=uP9KN0 The entire playlist can be found here: https://www.youtube.com/playlist?list=PLl-gb0E4MII0sGLCJeqDB3y63HZ6lM5LJ