Results 1 to 2 of 2

Math Help - novice question

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    1

    novice question

    Why do the sum of all numbers in any square / sum of square diagonal numbers = the square root?
    123
    456
    789
    1+2+3+4+5+6+7+8+9 = 45
    1+5+9 or 3+5+7 = 15
    I am mathematically challenged, an explanation in words or a link where I can learn more would be helpful.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    \begin{array}{cccccc}1 & 2 & 3 & \ldots & n-1 & n\\<br />
n+1 & n+2 & n+3 & \ldots & 2n-1 & 2n\\<br />
2n+1 & 2n+2 & 2n+3 & \ldots & 3n-1 & 3n\\<br />
\dots & \ldots & \ldots & \ldots & \ldots & \ldots \\<br />
(n-2)n+1 & (n-2)+2 & (n-2)n+3 & \ldots & (n-2)n+n-1 & (n-1)n\\<br />
(n-1)n+1 & (n-1)n+2 & (n-1)n+3 & \ldots & n^2-1 & n^2<br />
\end{array}

    The sum of all numbers is S_1=1+2+3+\ldots+n^2=\frac{(1+n^2)n^2}{2}

    The sum of diagonal numbers is
    S_2=1+(n+2)+(2n+3)+\ldots+[(n-2)n+n-1]+n^2=
    =(1+2+3+\ldots+(n-1))+n(1+2+3+\ldots+(n-2))+n^2=\frac{(1+n^2)n}{2}

    Now \frac{S_1}{S_2}=n=\sqrt{n^2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Number of cones in sphere, total novice
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: November 29th 2011, 09:59 AM
  2. Replies: 5
    Last Post: March 15th 2011, 01:03 AM
  3. novice needs help
    Posted in the Math Puzzles Forum
    Replies: 7
    Last Post: November 30th 2009, 01:46 PM

Search Tags


/mathhelpforum @mathhelpforum