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I need a calculator that accepts inputs using product notation, can compute the following, and can return the result in scientific notation:

$$\dfrac{\prod_{i=1}^{3.1536\times10^{16}}(52!-i)}{52!^{3.1536\times10^{16}}}$$

I have tried wolframalpha.com, desmos.com, and Excel. None of them can do the calculation. Is there another calculator that would work?

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closed as off-topic by Evil, Juho, orlp, ryan, xskxzr Aug 4 at 2:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about computer science, within the scope defined in the help center." – Evil, Juho, orlp, ryan, xskxzr
If this question can be reworded to fit the rules in the help center, please edit the question.

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There are absolutely huge numbers involved in this calculation, no wonder you won't get the result by simple numerical computation.

However,

Let $x = 52!$ and $y=3.1536\times 10^{16}$.

A crude lower bound yields: $$ \frac{\prod_{i=1}^y(x-i)}{x^y} \geq (1 - \frac{y}{x})^y \geq 1-\frac{y^2}{x} .$$ Putting numerical values and wandering on the safe side of approximations you get: $$1-\frac{y^2}{X} \geq 1-10^{-34}$$.

Thus,

$$ 1-10^{-34} \leq \frac{\prod_{i=1}^y(x-i)}{x^y} \leq 1 $$.

The value you are looking for is basically $1$.

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