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September 6th, 2015, 04:58 AM   #1
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Lightbulb let's see who is the fastest

Find the value of


$\displaystyle 2!!!!!!!!!!!!!!!!!!............................... ...........................!!!!!!!!!!!! \text{(Upto infinity)}$

Last edited by skipjack; September 6th, 2015 at 06:26 AM.
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September 6th, 2015, 04:59 AM   #2
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Is it me???
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September 7th, 2015, 10:47 AM   #3
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I have no idea what you are talking about. How do measure the time taken to look at that and say "that number does not exist"?

(No, your signature is not interesting.)
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September 7th, 2015, 09:53 PM   #4
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Quote:
Originally Posted by Country Boy View Post
I have no idea what you are talking about. How do measure the time taken to look at that and say "that number does not exist"?

(No, your signature is not interesting.)
The no. Does exist.
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September 7th, 2015, 11:52 PM   #5
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Well, $2! = 2$, so if we take factorials a finite number of times, we get
$$2!!!!...! = 2.$$
However, I have no idea what would happen with an infinite number of factorials (or even if the concept is well defined).
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September 8th, 2015, 10:04 AM   #6
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We can prove that it is true for every $n+1$ and hence it is valid upto $\infinity$
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September 9th, 2015, 01:27 AM   #7
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No. You can conclude that it is true for any positive finite number of factorials.
The problem I have is that it is not clearly defined for an infinite number of factorials.

One way to formally define it would be:


Find $\displaystyle\lim_{n\to\infty}a_n,$
where
$$a_1 = 2,\qquad\qquad a_{n + 1} = a_n!$$
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