Lot f be ertine Rnd K be a positive integer Suppose that there are M70 and e7o ouch that 15(e)

Q: If æ is an irrational number, then it is the case that sup{q E Q : q< x} < x.

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Q: Show if gcd(a, b) = 1 and a \x and b\x Then a b\x

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Q: It is given that (²1) = 4, (3) k 2 -(" + ²) Write and expression for = B, (x+1)= = C (where n, k, A,…

A: Use the properties of combination.

Q: )(2n) for conplex number sequance show that if lm En=1 then 3no fN such that for for Hn 7 no o Znto.…

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Q: Determine the number of coprimes of p5 below p for the cases p = 2,3,5 by listing them neatly. Also,…

A: The function counts the number of coprime integers less than n

Q: m(m-1) 2. 2. in E an mfm-l) n-i mintl) 8. 2. how can get rid of I only m (m-i) remavn so that with…

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Q: - 25 -dr (x – 4)(x + 1) Evaluate

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Q: Let a, = 1 and a₁ + a1 = n² + 2n, n ≥2. Evaluate S

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Q: snip

A: Given: A=2131-10 and B=102132   (a) To find: AB

Q: . Show that n! > 3ª for n> 7.

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Q: 18) What is the value of 2x ifx 8? 1 A) C) 2 B) D) 1 2.

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Q: 4. Knowing that 1 + 3 + 5 + …+ (2n – 1) = n², find 1++3 +5 + .…+ 135 =

A: Solution :   Given that  1 + 3 + 5 + ... + (2n - 1) = n2    -----(1)

Q: 3.2÷.8=

A: In math, long division is a method used for dividing large numbers into groups or parts. It breaks…

Q: 2 Find z. TVans form afthe f.llowing (a) {finwns

A: Calculate z-transform for n≥0: Zsinωn=∑n=0∞sinωnz-n               =12i∑n=0∞eiωn-e-iωnz-n…

Q: 19. Which of the following properties of Real Numbers is NOT true ? * a. Vx ER, x+0 = x b. Vx, y, z…

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Q: 5) Suppose that W1 < R" and W2 4 R". Prove (W1 n W2) < R"

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Q: It is known to be Q-N. Accordingly, show that QxQ ~ N.

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Q: र 11 22 (-1)" 2²", when 12) an MO

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Q: Find the length of (3et − 3, 4et + 7) for 0 ≤ t ≤ 1

A: To find the length

Q: 6 - 7- E= {x|x F = {x|x is G = {X/X {시 the whose name is Country American Continent. is the one of…

A: Using set theory concept.

Q: a. (f+g)(-4)

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Q: If X-N(50,10), P(X > 65) = ? O 1) 0.067 O 2) 0.033 3) 0.168 O 4) 0.832

A: The z-score can be calculated by subtracting the population mean from the raw score, or data point…

Q: e) There are two numbers, n = C orn = D, where C < D and f"(n) = 0 or f"(n) is undefined. Find C and…

A: Differentiate f(x)=x25(x-10) with respect to x using the product rule of differentiation to find…

Q: 3. Find all r so that r-1+r-2| < 5.

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Q: 1. Plot each of the following polar coordinates:

A: Given, To plot (5,5π3) and (2,-5π4)

Q: Lise a direct proof to show "fx's odd and y is even, anen x+1s odd."

A: The given statement is: "If x is odd and y is even, then x+y is odd" Result: Any odd number x can be…

Q: - 5. Prove that an integer n is odd if and only if n° – 3 is even.

A: Answer

Q: Let a, b and c be integers that satisfy 1 1 1 - - - - a b C |(A) 2022 (В) 2025 Find one possible…

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Q: 37. (1 + /9 – æ²) dæ -3 Answer 9 3+ 4

A: sin-1(0) = 0 sin-1(-1) = -π2

Q: Show that the following argument is invalid: 3XF(x) V VyH(y),Vw(H(w) - S(w)) E3y-H(y)

A: The first expression is ∃xFx∨∀yHy. That is this expression states that there exists x such that F(x)…

Q: 4x-100 over 10 minus 15-x over 5

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Q: Let * be the operation on the set of real number defined by a * b = 2a + 4b – ab. (a * b) * c = А.…

A: Operation * is defined by a*b=2a+4b-ab for all real number we have to find the value of (a*b)*c…

Q: Find all natural numbers m and n with properties GCD(m,n) = 8 and LCM(m, п) — 168. %3D

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Q: 4 + B Suppose A A:( ) then Kind ai/a2/as, au and a3 a1/a2/93,94

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Q: (P5, Page 16; Suppose that the number a se Proof bw C Prove that a <0 (You may have to

A: Introduction: Proof by contradiction (also known as indirect proof or the method of reductio ad…

Q: Assume that M = N₁ (h) + a₁h² + a₂hª + a3h6 + ... Then using Richardson extrapolation N4 (h) is of…

A: Given: Let us consider, M=N1h+a1h2+a2h4+a3h6+... Let's determine N4h using Richardson's…

Q: Which of the following is a false statement? OnC, = r!, Pr r!n Pr a combination is an arrangement of…

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Q: Show that for any neZ, n is either n= 4k n= 4ktI or n=Yk+2 n=4 K+3 or

A: Given below the detailed solution

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.