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 2 years ago

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.)

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

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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

Let x and y be integers. Prove that if x^2 + y^2 is a multiple of...

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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...

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Period Demand F1 F2 1 68 65 62 2 75 65 65 3 70 74 70...

Period Demand F1 F2 1 68 65 62 2 75 65 65 3 70 74 70 4 74 69 71 5 69 72 76 6 72 68 74 7 80 73 75 8 78 75 82 a. Calculate the Mean Absolute Deviation for F1 and F2. Which is more accurate? (Round your answers to 2 decimal places.) MAD F1 MAD F2 (Click to select)F1F2None appears to be more accurate. b. Calculate the Mean Squared...

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