Math CentralQuandaries & Queries


Question from debra, a student:

I just need to know how to solve the following problem without using a calculator: .999 ^ (500). I know the answer is .606, I just want to do it by hand since I can't use a calculator on my test.

(1 - .001)500; use a few terms of the binomial theorem, a bit messy though.



If you can use the fact that the limit of (1+x/n)n as n goes to infinity is ex, then with n = 500 and x = -1/2, you get that (1+x/n)n = .999500 should be about e-1/2 = 1/sqrt(e).
If symbolic form is good enough, you have it. You'd need numerical calculations to convert that to .606.


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