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Math Help - [SOLVED] Finding the limit of a sequence.

  1. #1
    Member ilikedmath's Avatar
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    Question [SOLVED] Finding the limit of a sequence.

    I need to find the limit of {(1 + \frac{1}{2n})^n}, and justify my answer.

    I know that \stackrel{\lim}{n\rightarrow\infty} (1 + \frac{1}{n})^n = e.

    Can I use \frac{n}{2} for my 'n,' so I get:

    \stackrel{\lim}{n\rightarrow\infty} (1 + \frac{1}{2(\frac{n}{2})})^\frac{n}{2}

    = \stackrel{\lim}{n\rightarrow\infty} (1 + \frac{1}{n})^\frac{n}{2}

    = \stackrel{\lim}{n\rightarrow\infty} [(1 + \frac{1}{n})^n]^\frac{1}{2}

    = \stackrel{\lim}{n\rightarrow\infty} e^\frac{1}{2} = \sqrt{e}

    Or is \frac{n}{2} not a legitimate choice since I am dealing with naturals?

    Thanks for your time,
    ilikedmath
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  2. #2
    MHF Contributor

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    That is the correct answer.
    You might have seen this \left( {1 + \frac{1}<br />
{{2n}}} \right)^n  = \left( {1 + \frac{{1/2}}<br />
{n}} \right)^n  \to e^{\frac{1}<br />
{2}}
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  3. #3
    Member ilikedmath's Avatar
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    Quote Originally Posted by Plato View Post
    That is the correct answer.
    You might have seen this \left( {1 + \frac{1}<br />
{{2n}}} \right)^n  = \left( {1 + \frac{{1/2}}<br />
{n}} \right)^n  \to e^{\frac{1}<br />
{2}}
    Thanks, Plato! You're such a lifesaver!
    It seems we're getting some spam posts on some threads here. I've noticed they're all 'newbies' too with a very few number of posts. How can we delete those spam posts?
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  4. #4
    Math Engineering Student
    Krizalid's Avatar
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    Quote Originally Posted by ilikedmath View Post

    It seems we're getting some spam posts on some threads here. I've noticed they're all 'newbies' too with a very few number of posts. How can we delete those spam posts?
    Don't worry, Moderators will take care of that.

    Meanwhile, if you see more spamming posts, report them.
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  5. #5
    Member ilikedmath's Avatar
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    Quote Originally Posted by Krizalid View Post
    Don't worry, Moderators will take care of that.

    Meanwhile, if you see more spamming posts, report them.
    All right, thanks. I just found the report button. I'll report those immediately!
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  6. #6
    Math Engineering Student
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    This one,

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