1. Prove by induction that for all n € N>1 we have (a) (b) (c) 2 +3 2.3 9+ (9 × 10) + (9 × 100) ++ (9 × 10-1) = 10" - 1 52n-1 + 1 is divisible by 6

Q: 10. Using the first principle of math induction, prove that, for n positive integer n³ + 2n is…

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Q: In the expansion of (2 + 4y?) a. How many terms are in the expansion after like terms have been…

A: We will find the answers of all parts using binomial expansion.

Q: mathematical induction

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Q: Use mathematical induction to prove that (n³ + 3n² + 2n) is divisible by 3 for all n > 1.

A: See the attachment

Q: Prove n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

A: We have to proff the question

Q: In (5 – x) – In (5 + x) = -In 9

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Q: 3. Using induction, verify that 12 + 3 + 5² + (2n – 1)² = n(2n–1)(2n+1) is true for every positive…

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Q: With induction, prove that 1*2 to the power of 0 + 2*2 to the power of 1 + 3* 2 to the power of 2 +…

A: To prove

Q: (2) Prove by mathematical induction that for all integers n > 0, the number 42n+1 + (21 · 33"+1) is…

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Q: Ci) Use the method of Mathematical Induction to show that for all positive integer values n21,…

A: The principle of mathematical induction is a technique of proving a statement or formula which is…

Q: se mathematical induction to prove that the following statement is true: n(4n+ 1)(4n+5) 3x5+7x9++…

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Q: Show that the the greatest common divisor gcd(16" – 4",17" – 2") is divisible by 3 for all n E N.

A: Consider the provided question,

Q: ) 6. Express the sum 9 + 28 + 65 + ... + (n'+1) using E-notation.

A: We have to find sum of series:

Q: 4. n(n+ 1)(n + 2) is divisible by 6

A: We have to check

Q: Use the Principie to prove the Ving 3n+1 – 1 is divisible by 2 for all n > 0

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Q: (i) Use the method of Mathematical Induction to show that for all positive integer values n21, (1+…

A: Solution of given problem is followed by

Q: For all integers n> 0, 32n – 1 is divisible by 8.

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Q: 17. Prove by induction that 1³+23++n³= (1+2+...+n)² for all positive integers n, that is, the sum of…

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Q: . Prove, using mathematical induction, that 13n – 8n is divisible by 5, for n ≥ 1.

A: Let us consider the statement is  P(n) : 13n - 8n is divisible by 5. For n = 1, 13n - 8n = 5 is…

Q: If k is a positive integer, what is the remainder when (k+ 2)(k³ - k) is divided by 6? aburitowd ned…

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Q: Which value can you use for n to show that the first step in a proof by mathematical induction of…

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Q: let n be an integer solution to the equation n2+an-b=0 (n>7) if the representation of a in base n is…

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Q: Use induction to prove that (2n + 1)² – 1 is divisible by 8 for each positive integer n.

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Q: (a) Suppose that there are k distinct positive integers that divide an odd positive integer n.…

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Q: Let M = Find formulas for the entries of M", where n is a positive integer. Hint: a formula such as…

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Q: 2. Prove that n(n + 1)(n + 2) is always divisible by 6

A: We have to show that the number nn+1n+2 is always divisible by 6 for all n∈ℕ. Let Pn=nn+1n+2 where…

Q: . Use mathematical induction to show that n Σ r=1 (2r − 1)² = 1² + 3² +5² + + (2n − 1)² = = n(2n −…

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Q: Translate a of n=1/8(n-1) to a recursive formula

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