10. Prove that (n) ≤ n/2 for n ≥ 8.

Q: 7. i) How many functions are there from the set {1, 2, 3, ...,k} where k is a positive integer, to…

A:

Q: n E(-1)* k + k)"-1, n2 1. k=0

A: The given value of ∑k=0n-1knkkm=0. The main objective is to detemine the value of ∑k=0n-1knk2+kn-1.…

Q: 6. Let a be a number written (in base 10) as ao 10⁰+ a₁ 10¹ + a₂. 10²+...+an. 10" where 0 ≤a < 10.…

A:

Q: Let X~ N(2, 9). Compute P(1 ≤ X < 7).

A: From the provided information, Mean (µ) = 2 Variance (σ2) = 9 X~N (2, 9)

Q: 6) If X is N(45,5) for i = 1, 2,..., 25; find: 25 (a) P (30 < (X-45) < 55) 221 b) P(30< (X -45) 2 <…

A: The objective of the question is to find the probability of two different scenarios for a normally…

Q: Let x be the set of all positive integers and d(min) = | = - = | show that (x,d) is not complete

A:

Q: 5. Let r > 1 be an integer such that 2" + 1 is prime. Show that r = 2" for some non-negative integer…

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Q: 11. What is the sum of all possible positive integers a, such that for any positive is an integer?…

A: Claim: n(n+2)(n+4) is always divisible by 3. Proof: we know, n = 0 or 1 or 2 (mod 3)    When, n = 0…

Q: Find the supremum and infimum of the set x € R:x = +(-1)" ,n e N} + (-1)" ,n e N}

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Q: 3.5. Let n E N. Prove that if n + ÷ < 2, then n² + n2 <4.

A:

Q: XA and x & f(x)}. Show Cim ƒ.) 38. Let a, b, c, and d be any real numbers such that a < b and c < d.…

A:

Q: 2. The set of all rational numbers in the interval (0, 1).

A:

Q: 5.80 Show that these facts are true. Use the definition of binomial coefficients to show that each…

A: We expand left hand side i.e. nCn nCn= n!/n!*(n-n)! We know that 0!= 1 so  nCn = n!/n! = 1 This…

Q: Prove that 6 divides n³ - n whenever n is a nonnegative integer.

A: In this problem we have to prove that  divides  where  is a nonnegative integer.

Q: Seaet =1+ e* + e3x + e(n+1)x enx +esx. n! sx € (0,e*) | ... 2 (п + 1)!"

A: we know that ex=1+x+x22!+x33!+........................+xnn!                      ..1

Q: 33. Let R be the set of all real numbers, x ER and n eN a n 2 2. If (1+ x) > 0, then which of the…

A: Option (C) II only is correct.

Q: prove that (1- (1/4))(1-(1/9))(1-(1/16))...(1-(1/ n2)) =(n+1)/2n for all integers n greater than or…

A: We have to prove that  (1- (1/4))(1-(1/9))(1-(1/16))...(1-(1/ n2)) =(n+1)/2 By mathematical…

Q: Let X-x²(18). Given P(7.015 < X <)-029th - then: a) 14.44 b) 10.865 c) 6.265

A: Let X~χα2( 18). GivenP(7,015 &lt;X&lt;χα2)=0.29To find the χ2(α) using the Excel software…

Q: 5. Identify the mistake(s) in the following "proof": Theorem: The sum of any two positive integers…

A:

Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

Q: 10. Evaluate | x In(x+12) « dr.

A:

Q: Let X~ N (24, 49), Find P( 10<X< 38)

A: Given sample are: 24, 49 Mean of these samples are: μ=24+492=36.5 Standard deviation:…

Q: 21. How many positive integers x are there such that 3x has 3 digits and 4x has four digits?

A:

Q: 9.56. In Z11, express the following sums and products as r], where 0 <r<11. a. [7] + [5] b. [7] ·…

A:

Q: 2. Prove: if an < bn for » 1, and an on Definition 3.3. 00, then bn - 0o. Base the proof

A: SEQUENCE Question

Q: Prove for all integers n, k, and r with n ≥k≥r that (O)(=O(-) Lify both sides.) n n- r

A:

Q: 43. Show that there cannot exist rational numbers a, b such that V3 = a+b/2.

A:

Q: How do I prove the following statements: (a) For all a, b, c ∈ Z, if a a. ● (O2) For all a, b ∈…

A:

Q: Prove the inequality V1+æ – 1 –+ < 6 on [0, 0). 8

A: Consider the given inequality in the given interval. Use the graphical approach to prove the…

Q: 6. Prove that 3" < n! whenever n is a positive integer greater than 6.

A: We need to prove that ,  3n &lt; n!  for every positive integer n greater than 6. We will use method…

Q: 1. A = {x | x is a Prime number such that x <50 } 2. C = {x | x is a square of integer less than…

A: Both the questions are solved below. We will use the concepts of Sets.

Q: 9. Let A = 0100 001 0 0001 0000 to Show that A" = 0 for n ≥ 4. 6]

A: Solution:

Q: 5) Given f(x) = V1 -x² , the range is: a) O (-∞; -1] b) O [-1, 1] c) O All real numbers d) O [[0,…

A: The graph is shown below: