Subject: irrational numbers
We have a little mathematical problem... we need some help proving e is an irrational number!
We don't feel very confident in our formulas, so if You have the time to give us a little explanation we would be very grateful!!!
Thank You very much!!
/"Students in trouble" (Peter and Jenny)
We asume that e is an irrational number, that e=(a/b) where a and b are positive "whole" numbers. We asume that e is an irrational number, that e=(a/b) where a and b are positive "whole" numbers. By using the Taylor-method for around x = 0. For every positive "whole" number n there is so that
We want to show that b*n!*Rn is a "whole" number for all n 1 and that b*n!*Rn 0 when
n approaches .
This will be a contradiction. We wan't to know why!!
What you are doing here is correct but you don't need a special form for the remainder. It is more direct to write since is a geometric series. Thus when n=b, is an integer but which is impossible.
Doug and Penny
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