Write each as a single factorial. i) 56*6! i) (n + 3)(n + 2)(n + 1)! i) (n² + n)(n - 1)!

Q: Prove by mathematical induction that the sum of cubes of three consequtive positive integers n is…

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Q: FACTORIAL The number of different ways to arrange n objects is given by n!= nx (n-1)x(n-2)x...x3x2x1…

A: Given: The number of different ways to arrange n objects is given by  n! = n×n-1×n-2×...×3×2×1

Q: Prove that N × N × N is countable. Does your argument generalize to the Cartesian product of k…

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Q: Show that for every integer n, n³ + 2 is not divisible by 4.

A: Here, we use rules of divisibility.

Q: 17. Expand using Pascal's Triangle or the Binomial Theorem. Be sure to show the setup. Then,…

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Q: Write each as a single factorial. i) 90*8! ii) (n² + n)(n 1)! iii) (n +1)!/(n -1)!

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Q: 3) (n² + 10n+18) ÷ (n+ 5)

A: To divide the following expression.n2+10n+18÷n+5

Q: Show that the the greatest common divisor gcd(16" – 4",17" – 2") is divisible by 3 for all n E N.

A: Consider the provided question,

Q: divisible by 3 for

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Q: How many 6-digit numbers have three even and three odd digits? (The first digit cannot be zero.)

A: It is given that a 6-digit number is to be formed which will have three even and three odd digits.…

Q: Disprove  For any integer n, n2 + 5 is not divisible by 5.

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Q: 1+1+5215+5102

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