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

Q: 3. Evaluate |(n + 1)! – (n + 2)!|, where n E N.

A: To evaluate n+1!-n+2!, n∈N.

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

A:

Q: !. 2. Find 100 irrational nember s between o andd 3. Find 50 rational numbers betwee and 2. 4. Fmd…

A: We know  2&lt;e&lt;3 So,   0&lt;e1000&lt;1100      as  e&lt;3&lt;10 So, 0&lt;e103&lt;1100 Define ,…

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: 14. Use the indirect method (contrapositive) to show that "If a + b is an odd integer, then a or b…

A:

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: If is an odd integer, show that n* + 4n2 + 11 is of the form 16k.

A: Firstly, we have to prove that n4+4n2+11 is in the of 16k for an odd integer n. for making the…

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 ||

A:

Q: 4. A student asserts that valid reasoning? = O because tends to zero. Is this n=1

A: Consider the given:limn→∞1n2=0

Q: What is the true value of proposition? 1. 6 is an even integer (True/False) 2. June 18, 2020 is…

A: 1) 6 is an even integer.          (True) 2. June 18, 2020 is Sunday (False) Because June 18, 2020 is…

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

A:

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

A:

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…

A:

Q: Consider the statement If n is even, then 4n² - 3 is odd. The contrapositive of the given statement…

A:

Q: 8- Evaluate 2 2- + 415 8 —— 25 + 10 16 + 125 (Infinity)

A:

Q: Problem2 Let n and k be integers with 1 ≤k≤n. Show that 2+2 ( 7 ) ( k ² ₁) = (²²+²7). 2 Σκ=1 - (²72)

A:

Q: Proposition. For all a, ne Z with n> 2, if a =4n 3n, then a =, 0.

A: To prove - For all a, n ∈ ℤ with n ≥ 2, if a ≡4n 3n, then a ≡n 0

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: 3) Two points are plotted on the number line below. 十+ -10 -9 -8 -7-6 -5-4 -3-2-1 十十+ 1 3 10 Which…

A:

Q: 2. Possible whenn A- Zero b. Negutive integer C- Negative Yational d- Positive integer

A: We know that Laplace transform of

Q: 21 Which of the following is equivalent to P(n+1, 3)? O n - n O n? +n O n + 2n – n О Зп + 3

A:

Q: If S = 1+2+4+ 8+ 16+ 32 + 64 + ... + 1024, then S = 2" – 1 where n =

A: Given: ∑r=0602r=2n-1 S=1+2+4+8+16+32+64+...+1024 Then S=2n-1

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.

A:

Q: Let o = (1,3,5,7,9, 10,2)(4,6,8)What is the smallest positive integer n such that o" = o-8? %3D

A: We have to find the smallest positive integer n such that σn=σ-8 where σ=1,3,5,7,9,10,24,6,8.…

Q: b>3 olmak üzere 2n+1 3n+1 13 eşitliğini sağlayan b sayısı 5n n=1 aşağıdakilerden hangisidir? (a) b=4…

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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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Q: Which of the following statements is FALSE? Select one: a. 7+11+ 15 + - + (4n+3) = 3+8+13++ (5n - 2)…

A:

Q: State the excluded values for each. 60x 1) 12x 702 2) 100 n+6n + 5 4) m+7 3) m +4m-21 n+1

A: