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


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


1 Answer 1


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


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: $$1-\frac{y^2}{X} \geq 1-10^{-34}$$.


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

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


Not the answer you're looking for? Browse other questions tagged or ask your own question.