This Sum Collapses Cleanly | Discrete Math | Number Theory | Induction | Summations | Dogmathic скачать в хорошем качестве

This Sum Collapses Cleanly | Discrete Math | Number Theory | Induction | Summations | Dogmathic

https://dogmathic.com/ In this video proof-by-induction walkthrough, we prove the clean summation identity ∑_{j=1}^{n} 1/(√j + √(j+1)) = √(n+1) − 1. We verify the base case n=1, state the induction hypothesis, split the sum at k+1, then rationalize using the conjugate and the difference-of-squares trick. The final cancellation reveals the telescoping structure hiding inside the radicals. If you have a non-induction proof, drop it in the comments.    • A Suspicious Equality That Is Actually Tru...      • Black Bag Factorials: The Sandwich Trick F...      • Discrete Mathematics      • Summations      • Induction Proofs      • Number Theory   Thumbnail: USS Silversides (SS-236) is a highly decorated World War II Gato-class submarine that sank dozens of enemy ships in the Pacific and is now preserved as a museum boat in Muskegon, Michigan. PROPERTIES AND CONCEPTS USED Summation Notation Mathematical Induction Base Case Induction Hypothesis Inductive Step Rationalizing Denominators Conjugates Difference Of Squares Square Root Properties Cancellation And Telescoping CHAPTERS 00:00 Introduction 00:45 Identity Setup 01:45 Base Case Algebra 03:00 Base Case Verified 04:30 Induction Hypothesis 06:00 Split The Sum 07:30 Substitute IH 08:45 Rationalize Last Term 10:15 Cancellation 11:45 Finish Induction 13:15 Thanks For Watching #math #discretemath #induction #summation #telescoping #algebra #squareroots #proof #dogmathic #induction #mathproof #summation #series #algebra #sigmanotation #identity