Prove each statement in 6--9 using mathematical induction. Do not derive them from Theorem 5.2.2 or Theorem 5.2.3. 6. For all integers n > 1, 2 +4+6+...+ 2n = n² + n. 7. For all integers n > 1, n(5n – 3) 1+6+11+16+ ... + (5n – 4) = 2 8. For all integers n2 0, 1+2+ 2² + · . . + 2" = 2"+1 – 1. - 9. For all integers n > 3, 4(4" – 16) 43 +44 +4° + .. + 4" = 3

Prove each statement in 6--9 using mathematical induction. Do not derive them from Theorem 5.2.2 or Theorem 5.2.3. 6. For all integers n > 1, 2 +4+6+...+ 2n = n² + n. 7. For all integers n > 1, n(5n – 3) 1+6+11+16+ ... + (5n – 4) = 2 8. For all integers n2 0, 1+2+ 2² + · . . + 2" = 2"+1 – 1. - 9. For all integers n > 3, 4(4" – 16) 43 +44 +4° + .. + 4" = 3

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Description: The previous proof was annotated to help make its logicalflow more obvious. In standard mathematical writing, suchannotation is omitted.in2Prove each statement in 6–9 using mathematical induction. Donot derive them from Theorem 5.2.2 or Theorem 5.2.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 23E: Let and be integers, and let and be positive integers. Use mathematical induction to prove the...

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