Approximating x^N for tiny x, large N - Science, Math and Philosophy Forum

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Approximating x^N for tiny x, large N

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11-09-2017 , 10:53 PM

gaming_mouse

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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?

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11-09-2017 , 11:06 PM

Aaron W.

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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 + ...

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11-09-2017 , 11:55 PM

gaming_mouse

Carpal \'Tunnel

Join Date: Oct 2004 Posts: 13,786

Thanks Aaron. Ofc, I guess I blanked for a moment there.

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