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Homework Help: Deriving the constant e using a sequence limit

  1. Feb 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Why does lim( (1+(1/n))^n ) = e?

    2. Relevant equations
    If a_n convergent to a, and b_n converges to b, then (a_n * b_n) converges to (a * b)

    3. The attempt at a solution

    The lim(1 + (1/n)) = 1.

    If you multiply (1 + (1/n)) by itself n-times, you get the equation (1 + (1/n))^n, so according to the statement under Relevant equations above, shouldn't the answer be 1^n, or just 1?

    Obviously it is e, b/c when you plug (1 + (1/n))^n into your calculator for larger values of n, you get closer and closer to e.
  2. jcsd
  3. Feb 17, 2012 #2


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    Science Advisor
    Homework Helper

    Hi Fibo's Rabbit! :smile:

    (try using the X2 and X2 buttons just above the Reply box :wink:)
    ah, but that only applies for the product of a fixed number of series …

    you're trying to apply it to an infinitely increasing number of series :wink:
  4. Feb 17, 2012 #3
    Ah, and it all makes a lot more sense now.
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