8. If A= 0 1 then A ( where k is any integer number) is

Q: The number of units in Z23[x] is O None 30 28 22

A:

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: 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…

A:

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 92n 3 6. cn 4 ac? Türkçe: c,…

A: To find the value of a from the given summation.

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: 3. Let, a, = 3, a2 = 4 and for n2 3, a, = 2an-1+ an-2 + nº+ 1, express a, in terms of n.

A:

Q: , Let a be a positive integer, where the positive difference of every two digits of a in base 10 are…

A: Here, For 1113,     | 1-1 | =0 , | 1-3 | = |-2| = 2 For 2000,     |2-0|= 2, |0-0|= 0 For 2022,…

Q: How many units are in Zn, where n 32547?

A: number of unit in ℤn=∅(n).

Q: The small positive integer n for which (1+i)=(1-1)" is =. ........ 8 4 12

A:

Q: If a = 2a - a² and b =1-(1-a), show that a = b for all natural numbers n. Assume that a, is a fixed…

A:

Q: Let c, ax, be nonzero real numbers such that e. Find a given that ac² n=3 16 Ch Türkçe: c, a, 3…

A:

Q: Need

A: Given that, a can be written as base 10 x= a0+10a1+ ......+10nar We know that, If a divides b…

Q: 3. Let a₁ = 2, a2 = 1, and for each natural number n > 2, let an 2an-1-an-2. Prove that for all…

A:

Q: 10. Let x be a real number. Prove that at least one of the numbers /2 – x or /2 +x is irrational.

A:

Q: If then A 1 = A = || = [6 0 0 030 0 7 2

A: Given is the matrix .The objective is to determine its inverse.

Q: 6. Let x and y be integer. Prove the following x + y is odd if and only if x² + y² is odd.

A:

Q: 2 2 Let A = Compute 412 - A and (412)A. 6-2

A:

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: 8. If a and b are odd integers, then 8|(a² – b²) -

A:

Q: 7. Let y be irrational and x ‡ 0 a rational number. Show that the product xy is irrational.

A: We will prove given statement by method of contradiction.

Q: "find A2, A−2, and A−k (where k is any integer) by inspection."

A: NOTE: Refresh your page if you can't see any equations. . use the diagonal matrix formula

Q: 9. Prove the following statements. For this question, upload your work as a pdf file (pictures of…

A:

Q: 5. Let m be the smallest positive integer such that m² + (m + 1)² ++ (m + 10)² is the square of a…

A:

Q: 14. Give a geometric explanation of why 2π/n 1-2 0 r² do = лr² 2 for any positive real number r and…

A: n2∫02πnr2dθ=πr2 For any positive real number r and any positive integer n. Prove this geometrically.…

Q: 2. What are the two largest positive integers n satisfying n - 1 | n²-A?

A:

Q: If x – 1 is an even integer, which of the following numbers must be odd? I. x(x - 1) II. 3(x - 1)…

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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)…

A:

Q: Show that if n is a positive integer, then fo(n) (26(n) $(2n) = if n is odd if n is even.

A: Given- n is a positive integer. To prove- ϕ2n=ϕn     if n is odd2ϕn   if n is even   Result Used-…

Q: Show that. 1 (n + 1)(n + 2) n=1

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.