Approximating x^N for tiny x, large N
Join Date: Oct 2004
Posts: 13,786
Consider:
Let x = 965604004910 / 965604004911
Calculate x^100000 to 2 or 3 decimal places of accuracy
You can't just use your favorite programming language's extended precision library, because the numbers get too big to handle.
I'm trying to figure out if there's a clever numerical method to solve problems like this?
Join Date: Sep 2002
Posts: 30,132
I think the binomial theorem is all you need here.
(1 + a)^n = 1 + n*a + n*(n-1)/2 * a^2 + ...
Join Date: Oct 2004
Posts: 13,786
Thanks Aaron. Ofc, I guess I blanked for a moment there.