This is what I'm trying to run:
########
var('n,i')
n = 36000
sum((factorial(n) / (factorial(n-i) * factorial(i))) * 0.00625**i *
(1-0.00625)**(n-i), i, 0, 250)
########
This is what I get: NaN
To be up front, I ran into this problem while trying this exact equation
with NumPy and SciPy. In searching for help it was agreed that I was
overflowing the Python data types, and among various answers was the
suggestion that I could simply use different data types from libraries more
suited to such numbers. That worked, but what I'm really searching for now
is a way to use Python for my math work that doesn't require I think about
whether variables are going to overflow.
SageMath seems to nearly work. I can do a sum with only the factorials, and
I get a huge number (which is good). I can do the sum with just the
fractional powers, and I get a minuscule number (also good). Multiplying
them manually in Sage, I get +infinity. I understand there are much
easier/smarter ways to use the binomial theorem, but at the time I needed
to solve for 'n' and the best way to do that (that I could figure out) was
to use the binomial formula. The code above is really just an example of
the problem.
Does anyone know what in particular is causing the sum to fail?
Much appreciated!
Chris
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