Prove that if the integers 1, 2, 3, . . . , 65 are arranged in...

Prove that if the integers 1, 2, 3, . . . , 65 are arranged in any order, then it is possible to look either left to right or right to left through the list and find nine numbers that are in increasing order

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Colby Messinger answered 1 year ago

prove 2 is a factor of (n+1)(n+2) for all positive integers

Prove that 1^3 + 2^3 + · · · + n^3 = (1 + 2 +...

Prove that 1^3 + 2^3 + · · · + n^3 = (1 + 2 + · · · + n)^2 for every n ∈ N. That is, the sum of the first n perfect cubes is the square of the sum of the first n natural numbers. (As a student, I found it very surprising that the sum of the first n perfect cubes was always a perfect square at all.)

Prove these scenarios by mathematical induction: (1) Prove n2 < 2n for all integers n>4 (2)...

Prove these scenarios by mathematical induction: (1) Prove n2 < 2n for all integers n>4 (2) Prove that a finite set with n elements has 2n subsets (3) Prove that every amount of postage of 12 cents or more can be formed using just 4-cent and 5-cent stamps

Prove that for all integers n ≥ 2, the number p(n) − p(n − 1) is...

Prove that for all integers n ≥ 2, the number p(n) − p(n − 1) is equal to the number of partitions of n in which the two largest parts are equal.

Prove that there exists integers m and n such that 15m + 12n = 3 Please...

Prove that there exists integers m and n such that 15m + 12n = 3 Please do not prove by assuming m=1 and n=-1, I'd like to prove by not assuming any actual numbers.

prove that the square of the product of 3 consecutive integers is always divisible by 12

Use induction to prove that 8^n - 3^n is divisible by 5 for all integers n>=1.

Year Salary (A) Salary (B) 1 65 55 2 65 57 3 65 59 4 67...

Year Salary (A) Salary (B) 1 65 55 2 65 57 3 65 59 4 67 62 5 69 64 6 72 67 7 74 69 8 77 72 9 79 75 10 82 78 11 84 81 12 87 84 13 89 88 14 89 91 15 89 95 16 92 95 17 92 95 18 94 95 19 94 95 20 96 99 1. Economics assumes people are interested in their rational self interest. Suppose a person works...

DISCRETE MATH 1.Prove that the set of all integers that are not multiples of three is...

DISCRETE MATH 1.Prove that the set of all integers that are not multiples of three is countable.

ID Affiliation Location Education Confidence 1 1 3 0 72 2 1 3 5 65 3...

ID Affiliation Location Education Confidence 1 1 3 0 72 2 1 3 5 65 3 0 4 5 66 4 0 1 4 78 5 0 3 1 81 6 1 2 5 81 7 1 1 2 83 8 1 3 3 74 9 0 4 0 78 10 0 2 2 85 11 0 1 1 85 12 1 3 5 69 13 1 2 0 69 14 1 3 2 79 15 1 4 1 82...

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