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(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.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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(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. Prove by Mathematical Induction, for all integers n 2 3, that the sum of the interior angles of ai n-sided convex polygon is 180(n – 2)°. OFocus W 19°C Cloudy 近
Transcribed Image Text:(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. Prove by Mathematical Induction, for all integers n 2 3, that the sum of the interior angles of ai n-sided convex polygon is 180(n – 2)°. OFocus W 19°C Cloudy 近
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