How do you get for ?

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- Jan 18th 2011, 03:34 AMcrossboneFactorial question
How do you get for ?

- Jan 18th 2011, 03:46 AMProve It
(with terms on each side of the inequality)

. - Jan 18th 2011, 04:28 AMcrossbone
I can see the proof, but how do you get the first line ie what idea comes prior to that? why not 2.1, 2.4 or pi?

nevermind. I got it. - Jan 18th 2011, 04:08 PMHallsofIvy
Fpr those who didn't "get it", both n! and have n- 1 factors (not counting the "1" in n!). Just compare the size of the factors. n! is the product of all numbers from n down to 2 while has all "2"s. 2= 2 while 3> 2 so 3(2)> 2(2), 4> 2 so 4(3)(2)> 2(2)(2), 5> 2 so 5(4)(3)(2)> 2(2)(2)(2), etc.