Prove each of the following statements using strong induction. (a) Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps. (b) Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

Q: Write a carefully constructed proof of the following theorem by using mathematical induction:…

A: Given that ∀n≥1, 1+21+22+......+2n=2n+1-1. We have to prove this by mathematical induction.

Q: Prove that 9|(43n+8) for every integer n ≥ 0.

A:

Q: Prove, USING MATHEMATICAL INDUCTION, the theorem: “If n is even, then n + 1 is odd.”

A: Statement: If n is even n+1 is odd. We need to prove the above statement using mathematical…

Q: Use induction to show that 1+3+5+...+(2n-1) - n for all natural numbers n.

A: We will use the method of induction to show that 1 + 3 + 5 + ... + (2n-1) = n2 for all natural…

Q: Use the method of mathematical induction to prove the following statement where n is a positive…

A: Mathematical induction.....

Q: Use mathematical induction to prove

A: Given that,

Q: Let n 2 1, z be a real number, and r 2 -1. Prove the following statement using mathe- matical…

A: Mathematic Induction: It is a technique which is used to solve the mathematical problem which is…