To determine The flaw in the given proof of induction. Every postage of three cents or more can be formed using just three-cent and four-cent stamps Basis step: We can form postage of three cents with a single three cent stamp and we can form postage of four cents with a single four cent stamp. Inductive step: Assume that j cents for all nonnegative integers j with j k using just three and four cent stamps. We can then form postage of k + 1 cents by replacing one three cent stamp with a four cent stamp or by replacing two four-cent stamps by three three-cent stamps.

Q: 1. Show that the principle of mathematical Induction implies that I is the Ieast positive natural…

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Q: Use mathematical induction to prove that for each nonnegative odd integer n: 2n+1 2 + 1)(n – 1) 24 |…

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Q: Use cases to prove that for all integer n, n2+3n+5 is odd.

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Q: Show that for every positive

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Q: Prove that the fourth power of any integer has the form 4k or 4k + 1 for some integer k.

A: We have to prove the following -  The fourth power of any integer has the form 4k or 4k+1 for some…

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Q: 3. Use induction to prove that 15"+2 + 162n+1 is divisible by 241 for every nonnegative integer п.

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Q: Fibonacci-

A: Let p(n) be the statement:P(n):Basic step: so, p(1) is true.Now assume that, p(n) is true [Strong…

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A: See the detailed solution below.

Q: . Use mathematical induction to prove each of the following: * (a) For each natural number n,…

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Q: 1 1 + 3*5 1 1 n ... 1*3 5*7 (2n-1)*(2n+1) 2n+1

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Q: Prove that for every ponitive integer a if aº – 6° is a prime for some positive integer 6 5 = 2 or 5…

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Q: Let k be a positive integer. Use induction to prove that (k – 1)"+1 +k2n-1 is divisible by k² – k +1…

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Q: Prove that n2 + 4 is not divisible by 3 for all integers n.

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Q: . Prove that for each natural number n, /3n +2 is not a natural number.

A: Let n be any natural number.  n=3m+k2   =3m2+6m·k+k2   =9m2+6mk+k2   =33m2+2mk+k2 Here, m and k are…

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Q: 5. Prove the following statements by indu (a) For all integers n20, the number 52n- 3" is a multiple…

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