Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By awkward

Math Help - Summation Proof with Pascal's Triangle

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    United States
    Posts
    3

    Summation Proof with Pascal's Triangle

    My class was given the task to proof the equation in the picture.

    I understand that it says any row, n, has a sum that is 1 less than the sum or all preceding rows, but alas I cannot proof it with an equation.

    Any help is appreciated!

    Summation Proof with Pascal's Triangle-1017122006.jpg

    I am sorry for bad photo quality, I tried to highlight variables using MS Paint
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1

    Re: Summation Proof with Pascal's Triangle

    Hi Hajmahkra,

    I can't make out the image in your post, but based on your description of the problem, it should help to know that the sum of the elements in the nth row of Pascal's triangle is 2^n. The standard way to prove this, in case you don't already know, is to start with the binomial theorem,
    (1+x)^n = \sum_{i=0}^n \binom{n}{i} x^i
    and then set x=1, with the result
    2^n = \sum_{i=0}^n \binom{n}{i}

    That doesn't solve your problem completely, but it should be a good first step. Maybe you can do the rest.
    Thanks from Hajmahkra
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. sum of (n+1)th row pascal triangle proof
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: April 7th 2010, 04:48 PM
  2. Pascal's Triangle
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 1st 2008, 12:02 PM
  3. Pascal's triangle
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: June 4th 2008, 10:37 PM
  4. Pascal's Triangle
    Posted in the Discrete Math Forum
    Replies: 10
    Last Post: May 31st 2007, 08:12 AM
  5. Pascal's Triangle.
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 27th 2006, 03:22 PM

Search Tags


/mathhelpforum @mathhelpforum