.. (a) Prove by mathematical induction that 9**2 – 8n – 17 is divisible by 64 for all positive integers n. (b) Hence, find the smallest positive value of a such that 90 – a is divisible by 64.

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A: We have to prove given expression using mathematical induction.

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Q: 2. Let an = 3n + 2 for n = 0, 1, 2, ... (i ) Find ao, a1 and a2. (ii ) Show that a2 = 4a1 – 3ao.…

A: Answer and explanation is given below..

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A: Explanation of the answer is as follows

Q: Prove, by induction, that n + 3n2 + 2n is divisible by 6, for n 2 0.

A: In this problem I have use mathematical induction method two times please read step by step.

Q: (b) Prove that any odd number is expressible in the form 4n + 1 or 4n + 3 where n is an integer.

A: Number System

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A: Proof by induction involves three step. Take the statement to be proved as P(n). First step is to…

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A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: 12. i)Prove by mathematical induction that: 9"- 1 is divisible by 8, for all positive integers n.…

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

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A: Take n =0 a0=00-12=0 hence it is true for n= 0 take n= 1 a1=11-12=0 So it is also true for n=1 check…

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A: As per our guidelines we are supposed to solve only one answer . Please repost another question as…

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A: we have to show that 5n-1 is divisible by 5 for all n belongs to Z+ by induction for n =1.

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Q: (a) Prove that for all integer n 2 1, 3|n(n² + 11).

A: a.          In the given problem we have to prove that for all integer n≥1, 3|n(n2+11). To prove…

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A: Given: 9) To prove 12+14+18+... + 12n = 2n-12n for positive integers n.

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A: According to the guideline, the first question can be solved. Please repost other questions…

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A: Disclaimer:Since you have asked multiple questions, we will solve the first question for you. If you…

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A: Prove 42n-15n-1 is divisible by 225 for all non-negative integers using mathematical induction.

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Q: (a) Prove that 82n – 12" is divisible by 13 for all nɛ N.

A: As per guidelines we are supposed to solve maximum one questions at a time.kindly post another…

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A: as per company guidelines we are supposed to answer only one question with maximum three subparts.…

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A: Solution of the problem as follows

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A: Principal Of Mathematical Induction There is a misprint in question number 7 we are providing you…

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A: Number