 |
| ||
| |||
|
| Math Central | Quandaries & 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.
Penny
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.
Claude
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.