1) Let x be a positive real number. Show by induction on n that (1+x)" > 1+ nx for all integers n > 1.

Q: mathematical induction

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Q: 3. Let a be an odd integer. Prove by induction that a² - 1 is divisible by 2+1 for every integer n ≥…

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Q: Show using induction that 5 divides 8n − 3n for all integers n ≥ 0.

A: Let P(n) be the statement for all integers n greater than equal to 0 Then, 8n-3n is divisible by 5

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Q: Use induction to prove that (2n + 1)² – 1 is divisible by 8 for each positive integer n.

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Q: Please use strong induction to prove that each integer n that is greater than 0 can be written as a…

A: The given data is: To prove that each integer n that is greater than 0 can be written as a sum of…

Q: Use mathematical induction to prove that the sum of the cubes of any three consecutive natural…

A: To show that sum of the cubes of any three consecutive natural numbers is a multiple of 9. Let us…