Proof By Induction
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Proof By Induction
In addition to such techniques as direct proof, proof by contraposition, proof by contradiction, and proof by cases, there is a fifth technique that is
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SOLVED:In every proof by mathematical induction, it is important that both parts of the Principle of Mathematical Induction be verified. For instance, consider the formula 2 4 8 ⋯ 2^n=2^n 1 1 a. Show that if we assume the formula is true for some positive integer k then the formula is true for k 1. b. Show that the formula is not true for n=1. c. Show that the formula is not valid for any value of n by showing that the left side is always an even number and the right side is always an odd number
SOLVED:In every proof by mathematical induction, it is important that both parts of the Principle of Mathematical Induction be verified. For instance, consider the formula 2 4 8 ⋯ 2^n=2^n 1 1 a. Show that if we assume the formula is true for some positive integer k then the formula is true for k 1. b. Show that the formula is not true for n=1. c. Show that the formula is not valid for any value of n by showing that the left side is always an even number and the right side is always an odd number
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SOLVED:In every proof by mathematical induction, it is important that both parts of the Principle of Mathematical Induction be verified. For instance, consider the formula 2 4 8 ⋯ 2^n=2^n 1 1 a. Show that if we assume the formula is true for some positive integer k then the formula is true for k 1. b. Show that the formula is not true for n=1. c. Show that the formula is not valid for any value of n by showing that the left side is always an even number and the right side is always an odd number
SOLVED:In every proof by mathematical induction, it is impo…
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