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I am trying to prove that in the equation: $$F_{i,n} = \prod_{0}^{n-1}𝑃_{𝑖−(𝑛+1)}𝑃_{𝑖−𝑛}$$ as $i > n$, $i > 1$, $n \ge 1$, $n \longrightarrow \infty$ and $𝑃_{𝑖−𝑛} \longrightarrow 0$, $$F \longrightarrow 0$$ as well.

In the aformentioned equation, P is a real number (actually probability of something), raning from 0 to 1.

Any idea how I might be able to prove the theory in mathematics apart from proving it based on empirical results?

P.S. I am a Research Scientist with Computer Science background, lacking knowledge in theoretical mathematics. So any help related to this topic would help. Thank you in advance. With Regards, http://somdipdey.co.uk/

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  • $\begingroup$ What is $P_{i-n}$? $\endgroup$
    – Aphelli
    Feb 13, 2019 at 11:22
  • $\begingroup$ Probability, ranging from 0 to 1. I will update this in the question as well. Thank you for your reply. $\endgroup$
    – Somdip Dey
    Feb 13, 2019 at 11:23
  • $\begingroup$ Okay, but is $-$ the actual substraction sign? Is $F$ a function of $i$ and $n$? If so, what are you taking the product of? $\endgroup$
    – Aphelli
    Feb 13, 2019 at 11:30
  • $\begingroup$ Yes, $F$ is a function. The product is of two probabilities, $P_i$ and $P_{i-1}$ and the product continues for $n$ numbers. $\endgroup$
    – Somdip Dey
    Feb 13, 2019 at 11:33
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    $\begingroup$ I am sorry if I have been unclear: I did not merely write that $F_{i,n} \leq 1$. I wrote that $0 \leq F_{i,n} \leq P_i$. $\endgroup$
    – Aphelli
    Feb 13, 2019 at 12:07

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