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How was e computed?

  1. Feb 24, 2004 #1
    How was "e" computed?

    The title says it all.
  2. jcsd
  3. Feb 24, 2004 #2
  4. Jul 23, 2004 #3


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    the number e is by definition the number e such that the integral of 1/x from 1 to e equals 1. thus any method of approximating integrals allows you to approximate e. i.e. if yuo show that the integral of 1/x from 1 to 2.7 is less than 1 you have shown that e is greater than 2.7

    another nice way is to use the taylor series for e^x, and plug in x =1, which gives e = the limit of the series 1 + 1/2 + 1/6 + 1/24 + 1/120 + ....+ 1/n!+....

    My freshman calc prof gave as an exercise to prove this way that e starts out as 2.718281828.... but i never completed it. i could not believe in those days that math took that much work!
  5. Jul 23, 2004 #4
    calculate [tex] \lim_{n\to\infty} (1+\frac{1}{n})^n[/tex]
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