Results 1 to 2 of 2

Math Help - Proof by induction?

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    10

    Proof by induction?

    Prove that

    {1+(1/1)}^1 x {1+(1/2)}^2 ...{1+[1/(n-1)]}^(n-1) = {n^(n-1)}/{(n-1)!}

    I assume this has to be done by induction, but I'm having trouble working it out.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by ashamrock415 View Post
    Prove that

    {1+(1/1)}^1 x {1+(1/2)}^2 ...{1+[1/(n-1)]}^(n-1) = {n^(n-1)}/{(n-1)!}

    I assume this has to be done by induction, but I'm having trouble working it out.
    There's actually no need for induction.

    \displaystyle \prod_{k=1}^{n-1}\left(1+\frac{1}{k}\right)^k=\prod_{k=1}^{n-1}\left(\frac{k+1}{k}\right)^k

    =\dfrac{2\cdot3^2\cdot4^2\cdots n^{n-1}}{1\cdot2^2\cdot3^3\cdots (n-1)^{n-1}}

    Notice all the cancellations...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof by induction that 4| 5^n - 1
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: May 17th 2010, 10:23 AM
  2. proof by induction
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 17th 2010, 07:11 AM
  3. Mathemtical Induction Proof (Stuck on induction)
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 8th 2009, 09:33 PM
  4. induction proof
    Posted in the Algebra Forum
    Replies: 7
    Last Post: November 1st 2008, 04:32 PM
  5. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: June 8th 2008, 01:20 PM

Search Tags


/mathhelpforum @mathhelpforum