>> The assymptotics of the central binomial coefficient is more subtle
>> matter
>> Andrzej Chrzeszczyk
>
> The limit:
> sage: maxima('limit(binomial(2*x,x)/2^(2*x)*sqrt(%pi*x),x,+inf)')
> 1
>
> shows that
>
> binomial(2*x,x)/2^(2*x) ~ 1/sqrt(pi*x) as x->+oo
>
This follows very easily from Stirling's Formula. But I suppose the
original question was not so much "what is the answer" as "can I get
the answer from system [xyz] without having to think"!
John
> Andrzej Chrzeszczyk
>
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