n Prove that (3i – 2) = ; (3n – 1) for all integers n > 1. - i=1

Q: Show that (2i – 1) (2n)! for every positive integer n!2" n. i=l

A: We have to solve given problem:

Q: Find the value of c if -226 Σ1+0 2 C = No decimal entries allowed.

A: summation (1+c)^-n from 2 to infinity converges only if |1+c|<1(1+c)^-n is a GP series. Use the…

Q: Consider the sum (3)² + (8)² + (13)2 + · . + (15n – 2)2. | m 1 1 m(т + 1)] and k2 = (m(m + 1)(2m +…

A: Consider S=32+82+132+ . . . .+15n-22

Q: 3. Prove or disprove. For n> 1, use mathematical induction to establish each of the following…

A: Let's say we need to prove a formula or a statement P(n). To prove this, we need to prove that The…

Q: (4b) Prove that there exists no positive integer x such that 2x < x² < 3x.

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Q: Let r be a real number and let k be an integer. We then define the binomial coefficient () by r(r-1)…

A: Given, r is a real number and k is an integer  The Binomial Coefficient rk by rk= r (r - 1) --- (r -…

Q: 2n+1+(-1)" Prove that for all integers n 2 0, 3.2"

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Q: The numerical value of xe dr is

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Prove that πd/n n = nτ(n)/2.

A: your question has a silly mistake, it should be πd|n d = nτ(n)/2. supposeτ(n)=r , where r be the…

Q: 7

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Q: 3. Prove each of these divisibility statements by mathematical induction. (b) (a) 8|52n +7 for all n…

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Q: (3c) Let n E Z. Prove that if n is odd, then 4|(n² – 1)

A: here is the proof

Q: A positive integer n is called superperfect if ơ(ơ(n) = 2n Show that 16 is superperfect.

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Q: use gauss's trick to determine R(n)=2+3+4+...+(n-1)+n+(n+1)

A: It is known that sum of first n numbers is n(n+1)2  that is  1+2+3+----+n=n(n+1)2 Gauss trick method…

Q: ove or disprove: There exists an integer a such that 14 (3a-5) and 21 (2a +

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Q: Prove that 3|(52n – 1) for all ne N.

A: We prove it by mathematical induction. 1st step We show that the statement is true for n = 1.…