4. Proof by induction:(a) Prove that 3 (2n+1 +5") for every integer n ≥ 1.n(b) Show that k-1 k(k+1)for every n > 1.n+1(c) For every n EN let Gn be a graph constructed according to the following procedure:Go consists of a single vertex vo and no edges.• Gn is obtained from Gn-1 by adding a vertex Un, picking k € {0, 1, 2, ..., n-1}, andadding an edge between vn and Uk.Show that Gn is a tree on n+1 vertices for every n E N, no matter what number k wepick in each step.

According to the guideline, the first question can be solved. Please repost other questions…

Answered: 4. Proof by induction: (a) Prove that 3…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 63RE

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4. Proof by induction: (a) Prove that 3 | (2n+1 +5") for every integer n ≥ 1.