Results 1 to 6 of 6

Math Help - Help me to prove or disprove this:

  1. #1
    Member
    Joined
    Jun 2007
    Posts
    77

    Help me to prove or disprove this:

    1. \sum_{i\ =\ 1}^n i = \left(\begin{matrix}{n+1}\\{2}\end{matrix}\right)
    Last edited by EquinoX; January 17th 2008 at 10:36 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,395
    Thanks
    1481
    Awards
    1
    {{ n + 1} \choose 2}  = \frac{{(n + 1)!}}{{2!\left( {n - 1} \right)!}} = \frac{{\left( {n + 1} \right)(n)}}{2} = \sum\limits_{k = 1}^n k
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jun 2007
    Posts
    77
    Quote Originally Posted by Plato View Post
    {{ n + 1} \choose 2}  = \frac{{(n + 1)!}}{{2!\left( {n - 1} \right)!}} = \frac{{\left( {n + 1} \right)(n)}}{2} = \sum\limits_{k = 1}^n k
    where did the (n-1)! disappear to?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,395
    Thanks
    1481
    Awards
    1
    \left( {n + 1} \right)! = \left( {n + 1} \right)\left( n \right)\left( {n - 1} \right)!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jun 2007
    Posts
    77
    Oh I see, I got one more question to ask though:

    Conjecture: The product of an even integer with an odd integer is even.

    Proof(Direct): Let a be an even integer and let b be an odd integer. Because a is even, a = 2p for some integer p. Because b is odd, b = 2q + 1 for some integer q. If ab is even, then there exists an integer r such that ab = 2r. Thus, ab = (2p)(2q + 1) = 2r. As ab is equal to twice r, ab must be even.

    Therefore, the product of an even integer with an odd integer is even


    What is actually wrong with this proof??

    My guess is because it tries to prove the other way around, it tries to proof if the product of two integer is even then one integer must be odd and the other must be even. Am I right??
    Last edited by EquinoX; January 17th 2008 at 02:29 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by EquinoX View Post
    anyone???????
    see rule 10 here

    Quote Originally Posted by EquinoX View Post
    Oh I see, I got one more question to ask though:

    Conjecture: The product of an even integer with an odd integer is even.

    Proof(Direct): Let a be an even integer and let b be an odd integer. Because a is even, a = 2p for some integer p. Because b is odd, b = 2q + 1 for some integer q. If ab is even, then there exists an integer r such that ab = 2r. Thus, ab = (2p)(2q + 1) = 2r. As ab is equal to twice r, ab must be even.

    Therefore, the product of an even integer with an odd integer is even


    What is actually wrong with this proof??

    My guess is because it tries to prove the other way around, it tries to proof if the product of two integer is even then one integer must be odd and the other must be even. Am I right??
    the problem with this proof is that it begs the question. that is, it assumes ab is even from the get-go. it doesn't prove this. the right way would be to expand 2p(2q + 1) and see if you can factorize it to the form 2r (here r is an expression that we can say is an integer, not a single variable)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove or Disprove the Following:
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 8th 2010, 05:35 AM
  2. Prove or Disprove
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: February 20th 2010, 10:53 AM
  3. Set Prove or Disprove
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: September 1st 2009, 02:08 AM
  4. prove or disprove
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 25th 2008, 07:41 AM
  5. Prove or disprove help
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 27th 2008, 08:06 PM

Search Tags


/mathhelpforum @mathhelpforum