The Limit of (1+1/n)^n

I heard our professor Dales say a cool thing in one of the lectures a few months back, and I only got around to writing it down now.

The question is simple: What does…

(1 + 1/n)^n

… tend to as n tends to infinity?

Here are two arguments:

1. The inside of the bracket goes to 1 as n goes to infinity. We”ll end up with 1 to a really big power, which is still 1. Therefore, the limit is 1.

2. The inside of the bracket is always slightly bigger than 1. As n goes to infinity, we’ll have something larger than one to the power of infinity, which is obviously infinity. Therefore, the the answer is infinity.

Which explanation is correct? You choose ;)

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5 Responses to “The Limit of (1+1/n)^n”

  1. Lance Says:
    May 20th, 2009 at 8:54 pm

    1 makes more sense, but wolframalpha says its infinity.

  2. Matt Says:
    May 21st, 2009 at 10:53 am

    Sorry, but that’s rubbish:

    http://www37.wolframalpha.com/input/?i=%281%2B1%2Fn%29%5En

    You need to look near the bottom.

  3. Vlad Says:
    May 21st, 2009 at 1:45 pm

    @Matt:

    Spot on :)

    @Lance:

    It was a trick question. Neither answer is correct :p

  4. George Says:
    August 2nd, 2009 at 8:01 pm

    it Eulers number guys, you’d find it in every math book

  5. George Says:
    August 2nd, 2009 at 8:01 pm

    but i admit that its some kind of magic, that it happens to be like that

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