FACTORIALS Dr. Shildneck.

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Presentation transcript:

FACTORIALS Dr. Shildneck

What Does Factorial Mean? N! (stated “n factorial”) is defined as the product of every consecutive positive integer, in decreasing order, from N to 1. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120

n! = (1)(2)(3)(4)…(n-2)(n-1)(n). Formal Definition If n is a positive integer, n factorial is defined as n! = (1)(2)(3)(4)…(n-2)(n-1)(n). *A special case of n! is 0! Which is defined to be equal to 1. 0! = 1

Order of Operations Factorials follow the order of operations. For example: 1. 2n! 2. (2n)!

Examples 1. Find the first five terms of the sequence defined by

Examples 2. Write the explicit rule for the following sequence. 6, 24, 120, 720, 5040, …

Examples 3. Evaluate.

Examples 4. Evaluate.

Examples 5. Simplify.

Examples 6. Simplify.

Assignment Worksheet – Assignment #2