Sarahisme Posted July 24, 2005 Share Posted July 24, 2005 Hi all again! I'm sure there is a simple answer/solution to this problem...or a way to do it anyway, i just can't seem to get it. why does this = 1/e? Thanks Sarah Link to comment Share on other sites More sharing options...
Yggdrasil Posted July 24, 2005 Share Posted July 24, 2005 Look up the definition of e, for example at Wikipedia: http://en.wikipedia.org/wiki/E_%28mathematical_constant%29 Link to comment Share on other sites More sharing options...
Sarahisme Posted July 24, 2005 Author Share Posted July 24, 2005 oh lol, so its just by definition ? Link to comment Share on other sites More sharing options...
matt grime Posted July 24, 2005 Share Posted July 24, 2005 it depends on what you take as your definiton of exp(x) i suppose, but it is a standard exercise in anaylsis to demonstrate that (1+1/n)^n converges to e (where we define e in some other equivalent way), and not too hard if you are familiar with analysis. Link to comment Share on other sites More sharing options...
Dave Posted July 25, 2005 Share Posted July 25, 2005 In the analysis course I took, we started with the familiar Taylor series of exp at 1: [math]e = 1+ 1 + \frac{1}{2!} + \frac{1}{3!} + \cdots[/math] We then went on to prove that the limit converges to this. It's not particularly hard, and I'm sure that most other Analysis courses approach it in a similar style. Edit: Just noticed matt's post makes it a little redundant, but never mind. Link to comment Share on other sites More sharing options...
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