Use induction to prove: for any integer n > 1, (6j – 4) = 3n² – n.j=1Base case1> (6j – 4) =3n – n =n = 1j= 1Inductive stepkAssume that for any k > 1E (6j – 4) =j= 1kwe will prove that (6j – 4) =j= 1kkE (6j – 4) = > (6j – 4)+j= 1j= 1%3DBy inductive hypothesisk2+ 5k+ 2=( 3k2+ 6k+ 3)-(k+ 1)= 3 (k+1)^2-(k + 1)

We shall prove the given sum using Principle of Mathematical induction which means that a ) first we…

Answered: Use induction to prove: for any integer…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 46E: Use generalized induction and Exercise 43 to prove that n22n for all integers n5. (In connection...

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Use induction to prove: for any integer n > 1, (6j- 4) = 3n“ – n. j=1