(i) Use the method of Mathematical Induction to show that for all positive integer values n21, (1+x)"-1 is divisible by x, where x is any positive integer. (ii) Hence explain briefly how you know that 4" -1 is divisible by 3. (iii) Hence deduce that 20"-5" - 4" +1 is divisible by 12 for all positive integers n21.

(i) Use the method of Mathematical Induction to show that for all positive integer values n21, (1+x)"-1 is divisible by x, where x is any positive integer. (ii) Hence explain briefly how you know that 4" -1 is divisible by 3. (iii) Hence deduce that 20"-5" - 4" +1 is divisible by 12 for all positive integers n21.

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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