Results 1 to 4 of 4

Math Help - Sequence problem

  1. #1
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1

    Sequence problem

    Find the limit of the sequence.

    a_n = (1 + \frac{7}{n})^{4n}

    \lim_{n \rightarrow \infty} a_n = ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
    From
    The raggedy edge.
    Posts
    782
    <br />
a_n = (1 + \frac{7}{n})^{4n}<br />

    a_n=((1+\frac{7}{n})^n)^4 \rightarrow \ (e^7)^4=e^{28}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1
    Quote Originally Posted by Showcase_22 View Post
    <br />
a_n = (1 + \frac{7}{n})^{4n}<br />

    a_n=((1+\frac{7}{n})^n)^4 \rightarrow \ (e^7)^4=e^{28}

    Can you show me the steps from

    ((1+\frac{7}{n})^n)^4 to (e^7)^4
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Showcase_22's Avatar
    Joined
    Sep 2006
    From
    The raggedy edge.
    Posts
    782
    (1+\frac{x}{n})^n converges to e^x as n \rightarrow \infty. This is a standard result:

    The power series for e is  1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}......  ...=(1+\frac{x}{n})^n .

    In this case, x=7 so we have (1+\frac{7}{n})^n \rightarrow e^7
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 24th 2010, 02:10 AM
  2. sequence problem
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 17th 2009, 11:57 AM
  3. Sequence Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 11th 2008, 11:59 PM
  4. Sequence Problem
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 19th 2008, 11:29 AM
  5. A sequence problem.
    Posted in the Calculus Forum
    Replies: 9
    Last Post: January 13th 2008, 04:25 PM

Search Tags


/mathhelpforum @mathhelpforum