11. What is the sum of all possible positive integers a, such that for any positive is an integer? n(n+2)(n+4) integer n>100, a (B) 2 (C) 3 (D) 4 (E) 6 (A) 1 O A C O D

Q: Let n denote an integer. Prove that 5|n and 7|n if and only if 35|n.

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Q: n 2n + 2 /2 n 2n k k=1 \k –1, п+1 n -

A: The objective is to prove that ∑k=1nnknk-1=2n+2n+1/2-2nn This theorem can be proved by induction,…

Q: I need specific help in reading a piecewise function and writing the domain and the range in…

A: We first begin with the definition of piecewise defined function.A piecewise defined function is a…

Q: 23. For any real number a, a ‡ 0, show that a +1 a +4 a +7 a +5 a+6 a +9 a -2 a +3 and a +8 | = 0, a…

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Q: Given that the expression (n²+n+1) n! can be written as a(n + 2)! + b(n + 1)! + cn! where a, b, c…

A: The main objective is to find the sum value.

Q: If n is a positive integer with (n + 1)(n + 3) is odd, then (n + 2)(n+ 4) must be a multiple of 1) 6…

A: Given:  (n+1)(n+3) is odd We will get an odd number from product of two numbers only if the two…

Q: Let n EU = Z and p(n): n² + n is an even integer. a. Write the following statement: (Vn) p(n). b. Is…

A: (a) Here, the given statement is: For ∀n∈U=ℤ, p(n):n2+n is an even integer.

Q: (n+1)! (n-1)! = 10n

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Q: For any real number a, a ≠ 0, show that a+4 a+7 a+5 a +8 = 0, a+6 а+9 a+1 a+2 a+3 and 4a7a 5a 8a =…

A: We are required to prove: a+1a+4a+7a+2a+5a+8a+3a+6a+9=0a4a7a2a5a8a3a6a9a=0aa4a7a2a5a8a3a6a9=0

Q: Show that P(n, 1) + P(n, 2) = (22) – 2 (2), for integers n ≥ 2.

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Q: (a) For every integer n, the number n² — n must be even. (b) For all real numbers a, a² < a¹. (c)…

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Q: the statement below true or false for n=1? ©George Mason University 2+ 4 + 6+ ... + 2n = n² + n + 1

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Q: Show that for positive integer n,

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Q: 5. (a) Prove the following proposition: For all integers a, b, and d with d 0, if d divides a or d…

A: To Prove :-  For all integers a , b ,d with d≠ 0, if d divides a or d divides b, then d divides the…

Q: k+4 n(3n +7) k(k +1)(k + 2) 2(n+1)(n+2) k=1

A: Given ∑k=1nk+4k(k+1)(k+2) To show  ∑k=1nk+4k(k+1)(k+2)=n(3n+7)2(n+1)(n+2)

Q: Q:- Show thet B(n, n) B( n+on+=2 1-40

A: The solution is given as

Q: a. 3.2F> Fn+1 for n23 [Solutions and final ans

A: We need to prove 2Fn&gt;Fn+1 Now, we have formula for fibonacci sequence is Fn=Fn-1+Fn-2

Q: Given any real numbers a and d, consider the expression (a + md) + (a + (m + 1)d) + (a + (m + 2)d) +…

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Q: let a=2+7i b=4-2i Choose the correct result of a/b*

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Q: A is the set of odd number greater than 5 and less than 23 n (A)=

A: A is the set of odd numbers greater than 5 and less than  23

Q: this

A: We use definition of t(n).

Q: Prove that 2n + 3n is a multiple of 5 for all odd n € N.

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Q: 2. The sum of three consecutive positive odd integers is always a multiple of (A) 3 (B)5 (C)7 (D)9…

A: