Question 1 For a positive integer n, True False gcd (2n, 6n) = n

Q: Find Im(z) if z(8 + i) = 7+ (384 + 448i)

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Q: Find 3 values of r n =120 o(n) such that

A: Ok

Q: Suppose we have o(n)= = 2 . What can you say about n?

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Q: n! %3D if n is non-negative integer and proof r-1 r>t

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Q: 1. Prove the following equality by induction: 1- 22 + 32 – 4? +. + (2n - 1)? - (2n)² = -n(2n + 1),…

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Q: n If E (ak + bk) 2n and n+1 k=1 E(ak – br) +, then ak = n n+2 k=1 k=1 3 2 5 2 O None 2

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Q: The statement 2n< n! is valid for For only n=4 All positive integers All positive integers n 2 4 All…

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Q: Question 5 Find all integers n >1 such that 1" + 27+...+(n – 1)" is divisible by n. |

A: To find all the integers n&gt;1 such that 1n+2n+...+n-1n is divisible by n Proof: Let…

Q: In your explanation of the other students follow up question regarding where (1/2) came from in part…

A: Given: At the beginning, there is Jane's starter with 50g of water and 50g of flour with gluten.…

Q: If α and β are two real numbers, we say that β is equivalent to α if there are integers a, b, c, and…

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Q: A-1 If A If A = || 18 01 00 9 then 1

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Q: Question 1 From the list below, choose the correct statements: O 17|0 5| 50 22| 11 O 4|(4n + 2)…

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Q: Prove that: n² + 3n 1 →> 2n² + 1 2 You may use any results from lectures, but you must state them…

A: (.) Given,                We find the limit.

Q: If a, b e Z such that a b then the numbers a and b are called relatively prime numbers if gcd(a, b)…

A: Consider the given statement. We'll prove the statement by contradiction. Let's the numbers are not…

Q: Question 11 (Зг+1) da x2-a-6 Evaluate: O None of these O 2 In a-3+In | a+2 |+C O In a-3+2 ln | a+ 2…

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Q: Find out the following: If A = {1,2}, then |p(p(A × p(A)))| = ?

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Q: 1+ Sn 2

A: To evaluate the integral of the given trigonometric function

Q: 11. Prove that every positive integer n can be expressed in the form n=4k or n=4k+1 or n=4k+2 or…

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Q: (c) Find an element h of S10 such that hog (1 8 10 2 7 3 6 4), = and write it in two-line notation.…

A: (c) In one-line notation, g can be written as        g = (1  6  9  3  10  8  7)(4  5)    Then,…

Q: QUESTION 3 Let P(x) is cold Q(x,y)=xisy. The universe of x is seasons, and the universe of y is…

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Q: Let T: ²->² be a linear transformation that maps u = Use the fact that T is linear to find the image…

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Q: Question 1 Is it possible for one of (oA) A 0 and o A ( e) to be true and the other false? No, they…

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Q: let a=2+7i b=4-2i Choose the correct result of a/b O (6-361)/20 O (-6+361)/20 O (-6-36i)/20 O…

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Q: Evaluate the following 5s L (8 – 2)2 -1 -

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Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

A: The binomial expansion of (a+b)^n is

Q: Question 3 Prove or disprove: 31 (2n² + 1) if and only if 3 m 3| n

A: Any integer can be written in form of 3k or 3k+1 or 3k+2 for some integer k

Q: (3x* – 1) dx + x°dy = 0; when x = 1, y = 1

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Q: Which of the following is a coefficient of x' in (2 - x)11, O -5280 O 5280 О -330 О 330

A: In the expansion of (a+b)n , the (r+1)th term is given by tr+1 = ncr.an-r.br

Q: Which of the above will have a value of 1? [Select] Which of 1-7 would be evaluated by [Select] 601…

A: It is given that n=50 and p= probability a single student passes the exam.

Q: j! j=0 4.

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Q: Prove the proposition that P(n): 1+4+42+.+4n. 40+1-1 %3D ... 3 ,n20.

A: To prove the given proposition, we take S=4+42+43+···+4n. Then we multiply S by 4 and subtract the…

Q: Show that E(r(r + 1) =- n(n + 1)(n + 2), n E N.

A: We have to show that ∑r=1n(r(r+1))=13n(n+1)(n+2)           ∀n∈ℕ

Q: Compute the following: N!(N-4)!

A: Note that n!=n×n-1×n-2×…×3×2×1. Consider the given expression N!N-4!. This can be written as…

Q: is a1 = 2, a2 =3, and an  = 5an–1 – 4an–2 for n > 2 expressed in explicit formula? true or false?

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Q: (1+i)²n n! n=0 evaluate

A: The function ex has the expansion ex=∑n=0∞xnn!. The complex number eix=cos x+i sin x.  This is…

Q: If the numberr of elements h=50 ৭০d । (6) = ५ and 1(5)3D41(h), then the numbor of elements -

A: Answer can be given using the simple concept of  probability.

Q: Evaluate |P(A)| if A={n: n is a prime number from 1 to 100}

A: To evaluate : PA if A=n : n is a prime number from 1 to 100

Q: 1 If the N(A) consists of all multiples of x = , then the rank of A 4 is: а. 3 O b. 2 O C. 4 O d. 1…

A: It is clear that from N(A)