JESTIC True or False: For all n EZ, n +5n +2 is even. True False

Q: perform the indicted operation simplifly the result p2+4pt-32t2/p2+3pt-18t2   x  p2-9p+18t2/…

A: Answer and explanation is given below

Q: Discrete Math  n = 2k for some integer k by definition of even. Write 4k2 + 5 in the form of even n…

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Q: (n-1)! Use Euler's theorem to prove that if n is an odd integer, then n divides 2 -1.

A: Using Euler theorem to prove it.

Q: Questions: Confirm that gcd(30,40) * lcm(30,40) = 30 * 40. Find integers a and b such that 30a…

A: The gcd(30,40) is 10 The lcm(30,40) is 120.

Q: What is the value of (n - 2) +n - 1 when n = 4? O 15 17 7

A: We have to find the value of (n - 2)2 + n - 1 when n = 4

Q: Find the binomial that completes the factorization. 5s4+5000st3= 5s(       )(s2-10st+1002)

A:

Q: Consider the statement, "For all integers a and b, if the product of a and b is even, then a is even…

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Q: 692 + 685 + 678 + 671 + ... + 6

A:

Q: 4 k=1 k²

A: This question can be solved using the concept of summation.

Q: n + 3n

A:

Q: 8. 2 (3a,+1 – 4b+1) 86. | n=1

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Q: (b) If a, b and c are integers such that b| a and b| c, then b | (2a – 3c).

A: We have to proof

Q: 2n+3 €2? For which integers nonnegative n is prove YOur answer

A:

Q: Show that (a) 8n −3n is divisible by 5 for all natural numbers n.  (b) n2 −n +41 is odd for all…

A: expansion of (a+b)n = hco an bo + nc1 an-1 b1 +.......... +ncn ao b n

Q: this

A: We use definition of t(n).

Q: 6.1 3m2- 2m +5 and m² + 3m-4 1*.. ...... 6.2 5n2-3n + 2 and -3n-4n + 5 From 2x- 7x² +x- 3 subtract…

A: We need to subtract the given expression:

Q: Drag the tiles to the boxes to form Match the pairs of equivalent expressions. (-14 + ) – (1 + ) (5…

A: first solve all the expression and the find the equivalence expression:…

Q: Let -3] A = |-4 –5 -2 -5 3 5 -2 Find minor(A)32- minor(A)32 =

A: Given that  a matrix A.  Here we have to find (A)32 .

Q: se indirect proof to show that, "If n is an integer and 3n + 2 is even, then n is even

A: Let us solve the classical algebra problem in the next step.

Q: n+1 n+3 n+ム ニ

A: To find the value of above infinite series first we will check the convergence of given series using…

Q: In

A: it is the telescopic sum

Q: Find 2(2k + 2). k-3 O 8+ 10+ 12 + 14 + 16+ 18; 78 8+ 10+ 12+ 14 + 16; 18 O 10+ 12 + 14 + 16+ 18; 8 O…

A: ∑k=38(2k+2)=(2×3+2)+(2×4+2)+(2×5+2)+(2×6+2)+(2×7+2)+(2×8+2)…

Q: Show that if n is an integer and 5n + 6 is odd, then n is odd. (Use contradiction.)

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Q: Briefly explain. what is the error in the proof of the claim: for every natural number n, n+2=n+4?…

A: Concept Used:(Principle of mathematical Induction) If Pn be the statement n is natural number to…

Q: For every integer n > 1, 2+4+6+ + 2n = n² + n.

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Q: By the mathematical induction, n(n - 1)(2n - 1) is divisible by 6. False O True

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Q: (5-V3)(3-V3) | Q3.Simplify fully 2 a+bv3 Give your answer in the form where a andb are integers.

A:

Q: What is wrong with the following “proof" of the "fact" that n+3 = n+7 for all values of n (besides…

A: Given: Let P(n) be the statement that n+3=n+7 The objective is to prove that P(n) is true for all n…

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

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Q: o 5 (10 - 2 3) + 8

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Q: (Proof) For any integer n, n² + n is even.

A: We know the product of consecutive integers in a even integer.

Q: 6x* + nx – 14x² + 2 is divisible by 2x + 1. The remainder is –2. Find the value of n. Justify your…

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Q: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

A:

Q: True or False. Briefly explain If p is odd prime then p divides 2p−1+(p−1)!.

A: Given: is an odd primeTo check:The prime divides  or not.Results used:Wilson's Theorem:For any…

Q: The sum of two integers with diff fit this description. 10

A: Given : To determine the two integers that will fit the condition            +          = -10

Q: algebriac proof of 8x+12=52

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Q: EX T I || = ง - X

A:

Q: n + 2 < −2

A: Given n+2&lt;-2

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.