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| 14 Mar 2017 07:41 PM |
| What does x approach, as you continue this recursive formula to infinity? x = #### # ####### # ####### # ########## (Yes, there is an answer.) |
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| 14 Mar 2017 07:42 PM |
| Or not. Thank you, roblox. |
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tengent
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| Joined: 12 Nov 2016 |
| Total Posts: 1006 |
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Tynezz
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| Joined: 28 Apr 2014 |
| Total Posts: 4945 |
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| 14 Mar 2017 08:33 PM |
| Isn't this just an infinite series? Just determine if the series converges and if it does, find it's value. |
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| 14 Mar 2017 09:30 PM |
| It is not a series. And if you try to plug this into a calculator, you will find that it's undefined. Here's a hint. The answer is not a real number. |
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Pinkerten
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| Joined: 03 Aug 2014 |
| Total Posts: 840 |
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| 14 Mar 2017 09:41 PM |
x = 2/pi -- easy * ln(2/pi -- tf is ln
* ln(2/pi -- stop this
* ln(...))) -- magic dots? |
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| 14 Mar 2017 10:03 PM |
^The dots means the recursion continues to infinity.
Clearly, nobody is going to find the answer, so I'll tell you, and prove it.
(Since roblox doesn't like for me to write slashes, I'll use a = 2 / pi.)
Okay, so x = a * ln( a * ln( a * ln(...))) off to infinity, so what difference would it make if we wrote x = a * ln(x)? Well, it wouldn't really. Well, now all we have to do is solve for x. (From this point on, I'll stop using a, because I don't need to write any 2 / pi) Well, we can just multiply both sides by pi, so we get pi * x = 2 * ln(x). We can of course use a logarithm property to get pi * x = ln(x^2). Now just raise e to the power of both sides. e ^ (pi * x) = x ^ 2. If you don't realize this by now, it's okay, but, what we have here is Euler's Identity! The imaginary unit is a solution for x. e ^ (i * pi) = (i ^ 2). So, the formula approaches i. I don't know about you guys, but this absolutely blew my mind. |
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Pinkerten
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| Joined: 03 Aug 2014 |
| Total Posts: 840 |
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| 19 Mar 2017 09:18 PM |
| ln( x ) is log( x )/log( e ) aka log base e of x |
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Tynezz
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| Joined: 28 Apr 2014 |
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| 21 Mar 2017 03:16 PM |
| cringe at op's username, reminds me of that thread about mp3 or something |
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KapKing47
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| Joined: 09 Sep 2012 |
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| 21 Mar 2017 03:33 PM |
| Pinker, In() from what I recall is the factorial of the number given (Look it up) basically... 5! = 5 # # # # # # # 1 If I remember correctly (Never had to use factorials before). |
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KapKing47
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| Joined: 09 Sep 2012 |
| Total Posts: 5522 |
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| 21 Mar 2017 04:54 PM |
Unsub, I thought it was last time I checked :/ Correct me
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cntkillme
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| Joined: 07 Apr 2008 |
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| 21 Mar 2017 05:36 PM |
ln(n) gives you the exponent to raise e to the power to get n.
math.exp(ln(n)) = n |
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KapKing47
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| Joined: 09 Sep 2012 |
| Total Posts: 5522 |
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| 21 Mar 2017 06:03 PM |
I must have been asleep then when I was using a calculator :O Srsly, I didn't even see the n! button on the calculator and now I checked and saw it... my bad.
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