7. Vn E 2Z, if n2 is odd, then n< 2 is a true statement True False

Q: п(n + 1)(n + 2) 4. If n e N, then 1.2+2.3+3·4+4·5+...+n(n +1) = 3

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Q: 7. Prove that if a, = 1, a1 = 4, and a, = 6a,-1 – 9an-2 for n > 2, then a, = 3"-(3 + n) for all n 2…

A: We have to prove the following result by using the principle of mathematical induction.

Q: The contrapositive of the statement "If n is a prime and n23, then n+1 is not a prime", is "If n+1…

A: Contrapositive of a statement "If p, then q" is "If not q, then not p." So, the contrapositive of…

Q: not use ai please

A: Explanation:1. Then, 3n + 4 = 3(2k + 1) + 4 = 6k + 7 = 2(3k + 3) + 1 (3)2. By definition of odd,…

Q: 4. Conclude that n2 n=1 ||

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Q: x² < 0 if and only if æ <0. O Either true or false O Neither true nor false O True O False 2)

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Q: 23n (n!)3 30. (3n)!

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Q: 1 2 3 + + 3! 4! 2! 1 =1- (п +1)! п If neN, then + - - - (п+1)!

A: The principle of mathematical induction: -Let P(n) be a given statement involving the natural number…

Q: 5. Prove that (n, n + 2) = 1 is n is odd and (n, n + 2) = 2 is n is even.

A: Suppose (n, n+2) = d =&gt; d | n and d | n+2 =&gt; d | (n+2) - n =&gt; d | 2 =&gt; d = 1 or 2.

Q: How do I prove: If n > 1 is a natural number then there is a prime number p such that p|n.

A: This is a theorem of real analysis in which we have to find that there is a p who divides n.

Q: could you explain if option 14 is correct: the one attached

A: As per the question, we are tasked with minimizing the cost of meeting daily workforce demands for…

Q: 6. If n is an even integer and k is an odd integer, then which of the following could be an even…

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Q: If n∈Z, then 4|n2 or 4|(n2−1).

A: First, we need to understand the problem. The question is asking whether for any integer n, either…

Q: Determine the set of values of n for which n²-1 n² +1 and are positive integers. 2 2

A: First, we simplify the given expressions. The expression 2/2 simplifies to 1, which is a positive…

Q: 5. Prove that (n,n+2) = 1 is n is odd and (n, n + 2) = 2 is n is even.

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Q: It is a fact that if n is any nonnegative integer, then 1-(1/2"+1) 1 1 1 1+=+ + + •+ 2 2² 23 1-(1/2)…

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