Clarissa is tearing her test (1 sheet of paper) into small pieces. She picks up a piece of paper and tears it into 4 or 6 smaller pieces. Prove that she can tear the test into any number of pieces greater than 8.

Q: - Use mathematical induction to prove the following inequality (1+x) ≥ 1+ Nx when x>-1 for all…

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Q: Let n be the number points scored by a team in a football game. What are the possible values of n,…

A: It is given that n be the number points scored by a team in a football game. It is asked to find…

Q: Use mathematical induction to show that the sum of the cubes of three consecutive integers is…

A: To Use mathematical induction to show that the sum of the cubes of three consecutive integers is…

Q: Use permutations to solve. From a cooler with 6 different kinds of soda, 4 are selected for 4…

A: nPr = n!/(n-r)!

Q: For what values of n is 3" > n³ ? Use induction to prove your answer.

A: We have the given statement is 3n>n3 For n=1 we see that 31>(1)3 3>1 This is true. For n=2…

Q: Use induction to show thatn 2 2, п Σ 1 1 i i=1 1 i + 1

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Q: Use induction to show that Vn > 2, 6| 7" – 1.

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Q: 2k > 1+ k

A: We have to prove 2k ≥ 1 + k for every natural number k

Q: use the mathematical induction to prove : 2" < n! < 3" , Vn E N* ,n 2 4

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Q: 1+ 3n 0

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Q: Using direct proof method, prove the following. If n is an even integer then n² + 11 is odd. Answer:

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Q: 2. Use the Principle of Mathematical Induction to prove for any natural number n that: 2 (1– )(1 n2

A: In order to prove a relation p(n) for all natural number n we follow some steps: 1. We check whether…

Q: Prove that for any n EN the expression 32n-2 -9 is divisible by 72. Do not use Mathematical…

A: The given number is: 32n+2-9=32n32-9=32n(9)-9=9(32n-1)=9((32)n-1)=9(9n-1)

Q: ) Fill in the blanks to complete the proof of the following statement: "For all integers n > 1, 5n?…

A: We need to prove "For each integer n≥1, 5n2+3n is even" In proof by mathematical induction, we…

Q: Describe the methods of proof by induction and proof by contradiction.

A: The main objective is to describe the methods proof by induction and proof by contradiction. The…

Q: (2) Conjecture a formula for the number of sub- sets of an n-set and prove it by induction.

A: Conjecture a formula for the number of sub-sets of ann-set and prove it by inductionIf S is any set…

Q: п(п+1)(2n+1) Use mathematical induction to prove that 12 +2² +...+n? for any = positive integer n.

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Q: 1. Proofs and definitions by induction: a. Show 3 | n³ – n for all n b. Define the set of powers of…

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Q: "For all integers a, b and c, if a | b and b | c, then a | (5b – 3c)"

A: 4. Given the integers a, b and c. To prove: If a/b and b/c, then a/5b-3c.

Q: 3 Use induction to prove: for any integer n ≥ 1, 3 evenly divides n³ + 2n.

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Q: (d) Prove by induction that 5 "– 1 is divisible by 5 for all n e Z +.

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

Q: 3. Let an be an odd integer for each integer n > 1. Prove that if n is odd, then the sum Laj is odd…

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Q: A shop gives gift cards in nominal 25 and 40k. determine the possible total amount that can be…

A: Proof at first, the amounts seem semi-random:

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

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Q: 5) Use induction to prove that 4" -1 is divisible by 3 for all integer n21.

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Q: Use the Principle of Mathematical Induction to show that the statement is true for all natural…

A: For n = 1 Now assume that p(n) is true for some n =k, that is

Q: Prove the following statement by mathematical induction. For every integer n 2 0, 7" – 2" is…

A: Brief answer is given below.

Q: Explain how to use mathematical induction to prove that a statement is true for every positive…

A: Mathematical Induction is a technique for proving certain types of mathematical statements.

Q: Use mathematical induction to prove that 1+ 2" 1. (Upload your solution.)

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Q: 2. Prove by induction that: for all n € Z+₁ 1+4+7+ ··· + (3n − 2) n(3n-1) 2

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Q: Q6 Use mathematical induction to show that n > 2n +1 for all integers n > 2.

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