Show that for all n € N, one has 1 2√n+1 <√n+1-√n<; 2√ñ

Q: Show that An, n > 5 is simple.

A: Sol:- To show that An, the alternating group of even permutations of degree n, is simple for n ≥ 5,…

Q: For some real numbers m and n, the list 3n2, m2, 2(n + 1)2 consists of three consecutive integers…

A: For some real numbers m and n, the list 3n2 ,  m2  , 2(n + 1)2  consists of three consecutive…

Q: Prove that there is no rational number whose square is 12.

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Q: Show that if n is any integer, then 3 divides n3 − n

A: To prove:  if n is any integer, then 3 divides n3 − n. Concept used: Here we shall use the identity:…

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: Which set consists the possible rational roots of x + 4x - 2x +8 0? A 11, 18 B. 11, 12, 14 C. 11,…

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Q: √3+√75= √3+√√25.3=

A: Solve the given

Q: why

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Q: Use a calculator to find a rational number r such that |r − π2| &lt; 10−4.

A: Consider the given information. |r − π2| &lt; 10−4 The absolute the function is defined as.…

Q: Prove that (A-1)-1 = A. %3|

A: Let A be inverse of matrix A. Then, by definition We know that

Q: Disprove the statement: There is a real number x such that xº +x* +1 = 2x².

A:

Q: If m and n are rational numbers such that √m +√n = √5+√24 ,calcule a possible value for m² + n²

A: Given that √m +√n = √5+√24 To calcule a possible value for m² + n²

Q: Find all integers n such that n| (2n+3). *

A: Given, n|(2n+3)     TO find, All integers n

Q: Rationalize the denominator of √a +2 --47 2√a-√b √a +2 2√a-√6 Assume that all variables represent…

A: For rationalizing the denominator, have to multiply surd of the denominator to both numerator and…

Q: Problem 5: Suppose that a die is rolled twice. What are the possible values that the following…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

Q: √2-1/2 is irrational

A: We need to find whether irrational or not.

Q: ndicate the least integer n for which (3x5 + x2)4 is O(xn).

A: Solved using the binomial theorem

Q: the real number line which equals 1 Qs-, n=1 " + ] ကျေ 18+

A:

Q: If x is an integer, what is the greatest value of x which satisfies 5 &lt; 2x + 2 &lt; 9?

A: First of all, consider the definition of an integer. An integer is defined as the whole…

Q: (d) Prôvé that the square of every prime number greater than 3 is one more than a multiple 24.

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Q: that if 3 divides the sum of the digits of n, then 3|n

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Q: Show that V3 +2/6 is an irrational number.

A: A rational number can be represented as pq, where p, q are integers and q≠0. If a number can not be…

Q: Evaluate |⊂(R)| if R={n: n is a factor of 500}

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Q: For each positive integer n, define an = ((2+√3)" + (2-√3)") 2 It is known that an is a positive…

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Q: Show that if r is a rational number, then 2r2+3r+ 1 is rational as well.

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Q: In P2, find all real numbers a such that x - ax +1-a? is in the span of x -2x+1, x-1,and3x -2x-1. Oa…

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Q: Indicate the least integer n for which (3x⁰+2x²)(x³ +3x) x+14x € 0(x¹).

A: Given: 3x6+2x2x3+3xx4+14x∈Oxn To find: Least integer n for which the given condition holds.

Q: ues of p will 3x(4x+3)=-p have non-real root

A: Given Equation 3x4x+3=-p The value of p is found such that the equation has a non-real root.