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.

Penny

If you can use the fact that the limit of (1+x/n)^{n} as n goes to infinity is e^{x}, then with n = 500 and x = -1/2, you get that (1+x/n)^{n} = .999^{500} 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.

Claude

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