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

A:

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

A:

Q: 8"-3 is a multiple of 5. In other words, prove that 8"-3"=5 for some i integer j.

A:

Q: 2. T Let n be a positive integer. Use mathematical induction to show that 1+8+27+ + n²³: .... =

A:

Q: Use mathematical induction to prove that: 3n ≥ 2n + 1 for n ≥ 1 discrete math

A:

Q: Prove by induction that 32n 1 is divisible by 8 for Vn 20

A:

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

Q: Use mathematical induction to prove that 3n+ 7n−2 is divisible by 8 for every non-negative integer…

A: The given statement is, Pn=3n+7n-2 Let us assume that the statement is true for n=1 P1=31+71-2=8 As…

Q: Which value can you use for n to show that the first step in a proof by mathematical induction of…

A:

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

A:

Q: Q3. By using mathematical induction, show that 52n – 1 is divisible by 24, for all positive |…

A: We need to show that 52n-1 is divisible by 24. We can solve this using induction method.

Q: Use the induction argument to prove that 1+2+ + n = n(n+1) 2 for all natural numbers n ≥ 1.

A:

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: Find all positive integers n for which n1º +1 is divisible by 10.

A:

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…