In the process of proving P(n) by induction, we need to assume that P(n) is true and show that P(n+1) is true. Indicate which line we used the assumption in the process of showing P(n+1) is true:

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Q: This problem is much harder than it looks. Use induction to show that n³ <3n Vn ≥ 1 Hint: you may…

A: For   So it is true.

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Q: A sequence a1, a2, a3, ... is defined as follows: a1 = 3, and ak = 4ak-1 + 2 for all integers k ≥ 2.…

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Q: Show by induction that 1+3 +5+ . + (2n – 1) = n² ...

A: See the attachment

Q: 1. Use mathematical induction or strong mathematical induction to prove the given statement. 1 (a).…

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Q: Show by induction that n? (n+1)² i=1 Note: by means of the mathematical induction demonstration…

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Q: b) For all ne Z+ show that if n ≥ 24, then n can be written as a sum of 5's and/or 7's.

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Q: 4. Use mathematical induction to show that for any integer n ≥ 0,8" - 2" is divisible by 6.

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Q: Use math induction to prove V n E N, P(n) is true, where P(n) is the claim + (2n – 1) (2n + 1) + (2n…

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Q: For each positive number n, let P(n)be the formula 1 1 (1+;)(1+ (1+– = n + 1. .. (a) Write P(1). Is…

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Q: Q2. Use induction to prove that for any natural number n , 2-1 = 2 – 2-".

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Q: 17. 1+3n 0.

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Q: Use the principle of mathematical induction to establish the given formula. n(n + 1)(2n + 7) Ek(k +…

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Q: n + n² 2.

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Q: Fibonacci-

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Q: Consider the property п(Зп + 1) P(n):2 + 5 + 8+ + (3n – 1) nE N | 2 (a) Copy down P(n). Then write…

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Q: Prove using induction that Σm-1(2m - 1) = n².

A: The given statement .The aim is to prove the statement.

Q: Use proof by induction to prove that: =-n°(n+ 1)? %3D r=1

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Q: (1 + x)" > 1 + nx

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Q: ite P(0). Is P(0) true? Write P(k). Write P(k + 1). In a proof by mathematical induction that this…

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Q: 5. Use mathematical induction to show that for any integer n ≥ 0,7" - 1 is divisible by 6.

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