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I start my pattern with the number $1$. Each term in the pattern is the previous term multiplied by a random real number in the set $(0, X]$, where $X$ is a real number. The pattern does not tend towards $0$, infinity, or negative infinity. Find $X$.

IamKnull
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Steven Kim
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  • What ideas do you have for approaching this? What kind of material do you know that seems relevant? This site can often give answers that meet you where you're at in your understanding - but only if you help us see what you already know. – Milo Brandt Sep 14 '19 at 02:55
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    A very similar question was posted 6 hours ago... Is this a hw problem? – Rushabh Mehta Sep 14 '19 at 02:58
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    It is not a homework problem. It's for a program I am writing. I am trying to find a range of random float numbers to use for my stock price simulation function that does not change the price on average. I probably should use a Monte Carlo simulation but I was wondering if I could do the way above. – Steven Kim Sep 14 '19 at 03:22
  • I know high school math and some calculus. I thought of (0, 2] at first, but quickly realized it tends the pattern towards 0 because the numbers below 1 shrink the pattern far more than the numbers below 1 increase it. Then I thought of e, which sounds like it might be right, but I have no idea how I'd be sure rather than it tending somewhere slowly. My only strategy really is guess and check. I don't know where I'd start a step by step solution. I can tell that as X increases, the probability of randomly picking a number below 0 decreases, at a rate of 1/X. – Steven Kim Sep 14 '19 at 03:39
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    This is the slightly older post of the same question: https://math.stackexchange.com/questions/3355435/absolutely-wonderful-numerical-phenomenon-who-can-explain – Gerry Myerson Sep 14 '19 at 03:55
  • That's a very strange coincidence. @DonThousand, I can assure you I found this problem by randomly writing code at work. And it had nothing to do with stock price simulation. :) – Jake Mirra Sep 14 '19 at 13:54
  • @JakeMirra What a strange coincidence. – Rushabh Mehta Sep 14 '19 at 15:36

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