Results 1 to 2 of 2

Math Help - Using the binomial expansion.

  1. #1
    Member
    Joined
    Aug 2009
    Posts
    94

    Using the binomial expansion.

    Any faulty logic?

    Prove: if a>1, (a^n)/n --> infinity.

    Since a>1 we can write:

    a = [(1 + k)]/ [n^(1/n)];

    n*a^n = (1 + k)^n;

    n*a^n =1 + nk + [n(n -1 )(k^2)]/2!+.....;

    So, a^n =1/n + k +.....;

    >1/n + k;

    >M, for M>0 for say 1/n > M.

    Is there a problem here since n < 1/M? Or, does this still imply n > M, so it doesn't matter?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by cgiulz View Post
    Any faulty logic?

    Prove: if a>1, (a^n)/n --> infinity.

    Since a>1 we can write:

    a = [(1 + k)]/ [n^(1/n)];

    n*a^n = (1 + k)^n;

    n*a^n =1 + nk + [n(n -1 )(k^2)]/2!+.....;

    So, a^n =1/n + k +.....;
    At this step you should have,
    \frac{a^n}{n} = \frac{1}{n} + k + \frac{1}{2}k^2(n-1) + ... \geq \frac{1}{2}k^2(n-1)

    Now certainly, \frac{1}{2}k^2(n-1)\to \infty.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Binomial expansion
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 6th 2011, 11:20 PM
  2. Binomial Expansion
    Posted in the Pre-Calculus Forum
    Replies: 11
    Last Post: July 10th 2010, 10:00 PM
  3. binomial expansion help?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 15th 2009, 09:21 AM
  4. Binomial expansion
    Posted in the Algebra Forum
    Replies: 4
    Last Post: August 12th 2009, 06:24 AM
  5. Replies: 6
    Last Post: May 1st 2009, 11:37 AM

Search Tags


/mathhelpforum @mathhelpforum