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e raised to the power of 1 Billion vs 1 Billion Factorial.

by Crazy Guy
(USA)











































Which result is greater in value? I'm just curious of what the answers could possibly be? Is this a valid question? I'm a guy with too much curiosity but little $$$! There is no commercial value in this at all! How much do you want? What I can contribute would be an insult for someone who has the intelligence to answer! Am I wasting your time? Most likely! You don't have to answer if you don't feel like doing it! I still thank you in advance, no offense!

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Apr 02, 2010
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Exponents vs Factorials
by: Staff

The problem


Which result is greater in value? I'm just curious of what the answers could possibly be? Is this a valid question? I'm a guy with too much curiosity but little $$$! There is no commercial value in this at all! How much do you want? What I can contribute would be an insult for someone who has the intelligence to answer! Am I wasting your time? Most likely! You don't have to answer if you don't feel like doing it! I still thank you in advance, no offense!

The solution

Hi Crazy Guy,


1 billion factorial is the greater number by far.



You can probably use various mathematical functions (such as the gamma function) to compute the large values you are interested in.

However, you can see how this would work out if you compute (and/or plot) the results for low values of n

e = The Euler constant (2.71828...), the base for the natural logarithm




n; e raised to the power n; factorial of n


n; e^n; n!

n = 3; 19.90; 6
n = 4; 53.94; 24
n = 5; 146.17 ; 120
n = 6; 396.11; 720
n = 7; 1,073.46; 5,040
n = 8; 2,909.07; 40,320
n = 9; 7,883.58; 362,880
n = 10; 21,364.51; 3,628,800
n = 11; 57,897.82; 39,916,800
n = 12; 156,903.09; 479,001,600
n = 13; 425,207.37; 6,227,020,800
n = 14; 1,152,311.97; 87,178,291,200
n = 15; 3,122,765.43; 1,307,674,368,000
n = 16; 8,462,694.32; 20,922,789,888,000




Staff
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