Re: e is irrational,
- From: Stephen Montgomery-Smith <stephen@xxxxxxxxxxxxxxxxx>
- Date: Sun, 24 Sep 2006 02:50:26 GMT
vsgdp wrote:
My book gives proof that e is irrational, but I don't follow a step. They get the inequality:
0 < (2k-1)! * (1/e - s_(2k-1)) <= 1/2, for k>=1
where s_n = sum( (-1)^k / k!, from k = 0 to n).
They say (2k-1)! * s_(2k-1) is always an integer. Why?
Multiply it out term by term and see that each term is an integer. (Even the Greeks knew that one!)
.
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