2- Using Direct proofsprove if odd intege mis an even integer then mn is also an even integer
Q: 6 First Last Prove that 2 1² +2²+...+n² = n(n+i) (²n+1)/6) for positive integer. n. www
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Q: Prove that 1– 2+2² – 2° + -.-+(-1)"2"=2**1 for all nonnegative integers n.
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Q: Establish formula for the sum of First n odd positive integers and Prove it by using Mathematical…
A: Let 2n-1 represent any odd number , where n is a natural number.We need to find the sum of the…
Q: prove or disprove: the product of any odd number and any even number is even.
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Q: Use a direct proof to show that the product of two odd integers is odd.
A: Introduction: A direct proof is a series of statements, the final of which is the conclusion to be…
Q: Prove that every positive integer n>1 has a prime factorization.
A: Prime factorization is a way of expressing a number as a product of its prime factors.
Q: IM- Prove that n(n+ 1)(2n + 1)
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Q: Prove that the sum of the 1st natural n numbers = n*(n+1)/2
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Q: Determine whether the statement is true or false. Justify your answer with a proof by Direct Method…
A: The product of any two integers is odd. - True
Q: 1. Using proof by contradiction, prove Let n be an integer. If n- is even, then n is even.
A: Given: Let n be the integer. To prove : If n2 is even, then n is even.
Q: Establish formula for the sum of first n odd positive integers and prove it by using mathematical…
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Q: 1. Prove that the negative of any even integer is even. 2. Prove that the difference between an even…
A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…
Q: 75. Prove that the sum of an even integer and an odd integeris odd.
A: sum of an even integer and an odd integer is odd.
Q: Prove that for all divides natural numbers nt 7^-2^.
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Q: 9. Prove that there are as many positive real numbers as there are real numbers.
A: Consider the set X and Y. Then we said that |X| = |Y| if there exists bijective function from X to…
Q: Prove that for any 9 consecutive natural numbers, there exists one number that is prime to the other…
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Q: 3) Prove that there do not exist two rational numbers whose sum is irrational.
A: To prove: There do not exist any two rational numbers such that their sum is irrational.
Q: 2. Prove that n + 100 > 3" if n is a positive integer with 1 < n < 3. (Hint: Proof by cases)
A: Concept:
Q: 3. Prove that 2" > n For all nuatural numbers
A: Solution
Q: prove that "The Sum of two odd numbers is even: using direct. Note:- 1 want the ansawer on a paper.
A: The sum of two odd numbers is even. Proof : Properties odd and even integer. If…
Q: fermat's theorm states, if p is prime & a is a positive integer not divisible by p then-------- and…
A: Fermat's Theorem: If p is a prime and a is a positive integer and not divisible by the prime p, then…
Q: 3. Prove that the sum of any two rational numbers is a rational number
A: Consider ab,cd are rational numbers with a, b, c, d are integers. Now add these two numbers ab+cd…
Q: Q1 Use mathematical induction to prove that (-5)"+1 – 1 3 + 3 * (-5) + 3 * (-5)² + 3 * (-5)³ + .… +…
A: Given equation is, 3+3(-5)+3(-5)2+3(-5)3+......+3(-5)n=(-5)n+1-1-2
Q: Use indirect proof to show that if n is an integer and n^3 + 5 is odd, then n is even.
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Q: 22. What is the least upper bound property for nonemptysubsets of real numbers? Does the least upper…
A: Least upper bound property: Every non empty subset of real numbers which is bounded above has a…
Q: Find all positive integers n such that 2" – 1 | 3" – 1. - -
A: Given 2n-1|3n-1 , for n∈ℤ+ To find if the statement is true.
Q: - 5. Prove that an integer n is odd if and only if n° – 3 is even.
A: Answer
Q: Let 2k +1 be a prime number. Prove that then k = 0 or k = 2" for some n > 0. %3D
A: Solution:- Let 2k+1 be a prime number k=0 or k=2n for some n≥0 For, k=0 2k+1=20+1 2k+1=1+1…
Q: . show that for every positive integer n, if n^2+2 is prime then n is a multuple of 3. Is the…
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Q: Prove that n2+n is even for all positive intrgers n 1.by using parity arguments (ie. concept of…
A: We have to prove that n2+n is even.
Q: 11. Prove that the of product of 2 even integer is even.
A: The proof for the given statement is below.
Q: Suppose x is a fixed real number with x 2 -1. For n2 1, prove using mathematical induction: (1+ x)"…
A: Here we will show that given statement is true by mathematical induction method.
Q: Prove that 2 - 2 · 7 + 2 · 72 – ... + 2(-7)" = (1 – (-7)n+1)/4 whenever n is a nonnegative integer.
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Q: Prove or disprove: If three consecutive integers are multiplied together, and the second in order of…
A: We first look out some examples to understand the fact- choose three consecutive numbers be 1,2,3.…
Q: Prove that 2n>n2 if n is an integer greater than 4.
A: According to the given information, it is required to prove the given statement.
Q: Prove that any integer greater than or equal to 48 can be represented as the sum of nonnegative…
A: Principle of mathematical induction: For each and every natural number n, mathematical induction is…
Q: 4. A property that, two consecutive positive integers are relatively prime. Consider any two…
A: Two consecutive numbers are said to be relatively prime or coprime numbers if they have no common…
Q: 5) Prove that the sum of two fourth powers of integers can never be three more than a multiple of 4.…
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Q: (b) Prove that 2m ≤ m! + 2 for m ¤ N. (c) For any nonzero real number x, prove ---3 i=1 = 1- x -n
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Q: - Prove that if n is an integer, then n = +. (Hint: use the proof by cases with respect to even and…
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Q: Prove using mathematical induction that for every nonnegative integer n. ¡(i + 1) +1 (If n = 0, the…
A: Answer
Q: Prove 8^ +l is composic for any poSitive integer n.
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Q: yields a true statement when n is replaced by any positive integer.
A: The above statement is true. Step-2 i explained in detailed explanation
Q: Use mathematical induction to prove 8^n − 1 is a multiple of 7 whenever n is a positive integer.
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Q: Prove that ifnis an even integer then5n2+ 10is a multiple of 10
A: We need to prove that if n is an even integer then 5n2+ 10is a multiple of 10.
Q: 3. Prove that 0 divides an integer a if and only if a 0.(In your proof. you can freely ILNE your…
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Q: Fermat's theorem is not true for some prime number. اختر واحد
A: False
Q: 8. Use a direct proof to show that the sum of two rational numbers is rational.
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Q: 5. Use direct proof technique to prove the following theorem: "If n is an odd integer, then n³ + 1…
A: Since you have asked multiple question, we will solve the first question for you. If you want any…
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- 4. show that for every positive integer n, if n^2+2 is prime then n is a multuple of 3. Is the converse true> Justify.. A box contains 2 red marbles and 98 blue ones. Draws are made at random withreplacement.In ________________ draws from the box, there is more than 50% chance for a redmarble to appear at least once. Fill in the blank with the smallest integer numberthat makes the statement true.A $150 eReader comes with a warranty from an electronics business that covers theft (T) and accidental damage (AD) . Due to the high expense of repairing an eReader, it is more cost-effective for the business to provide the customer a complete refund to go toward another one. There is a 5.1% possibility that an AD (Accidenal Claim) claim will be made in any given year. Assume there can only be one claim made (not one of each type).Customers who report an eReader as stolen will get a reimbursement for 80% of the item's full price. A Theft (T) claim is likely to be submitted 3.5% of the time in any given year.What is the anticipated financial benefit or loss for the firm on each contract if the warrantee costs $15.95 for a year?(NOTE: Keep in mind that regardless of whether a claim is made, the consumer will pay for the warranty upfront.)
- the researcher wants to determine if more than 50% of the packs of junk food contains sodium of at least 70mg. 12 packs were randomly selected. based on the samples, 10 packs contain sodium of at least 70mg while 2 contain of less than 70mg. is z-test can be used as an alternative to binomial exact test since nPo & n(1-Po) are sufficiently large (both at least 5)?Fasteners used in aircraft manufacturing are slightlycrimped so that they lock enough to avoid looseningduring vibration. Suppose that 95% of all fasteners passan initial inspection. Of the 5% that fail, 20% are soseriously defective that they must be scrapped. Theremaining fasteners are sent to a recrimping operation,where 40% cannot be salvaged and are discarded. Theother 60% of these fasteners are corrected by therecrimping process and subsequently pass inspection.a. What is the probability that a randomly selectedincoming fastener will pass inspection either initiallyor after recrimping?b. Given that a fastener passed inspection, what is theprobability that it passed the initial inspection anddid not need recrimping?What is the solution to the recurrence relation: Tn=5nTn-1+6 with T0=3?
- A constructor has two subcontractors for his excavation Experience shows that in 60% of the time, subcontractor A was available to do a job, whereas subcontractor B was available 80% of the time. Also, the contractor is able to get at least one of these two subcontractors 90% of the time. Suppose EA denotes the event that subcontractor A is available, and EB denotes thatsubcontractor B is Are EA and EB statistically independent? Explain. Are EA and EB mutually exhaustive? Explain. Are EA and EB collectively exhaustive? Explain.A random sample of size n = 100 is taken from an infinite population with the mean μ = 75 and the vari-ance σ2 = 256. (a) Based on Chebyshev’s theorem, with what probabil-ity can we assert that the value we obtain for X will fall between 67 and 83? (b) Based on the central limit theorem, with what proba-bility can we assert that the value we obtain for X will fall between 67 and 83?In Stat 2 exam, a Stat Faculty wishes to arrange the chairs of 5 students such that 2 notorious students who are always caught cheating, will not seat together. In how many ways can this be done?