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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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We need to use induction to show and prove the attached problem. I know that we need to prove the base case is true, assume true for n, then show for n+1. However I am not sure how to use induction for this. I did find that we have multiple cases that do prove to be true.

For n greater than or equal to 24, we have the following base cases for n:

24: (5 x 2)   + (7 x 2),

25: 5 x 5,

26: 5 + (7 x 3),

27: (5 x 4) + 7,

28: 7 x 4

29: (5 x 3) + (7 x 2)

30: 5 x 6

31: (5 x 2) + (7 x 3)

What seems to be the pattern based on these above base cases, and how would we show induction here?

b) For all n € Z* show that if n ≥ 24, then n can be written as a sum of 5's and/or 7's.
Transcribed Image Text:b) For all n € 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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