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Posers and Puzzles

Posers and Puzzles

  1. 15 Oct '03 02:16
    Do you know that:

    Sum - odd numbers
    1=1
    1+3=4
    1+3+5=9
    1+3+5+7=16
    1+3+5+7+9=25
    ....

    Square roots
    The square root of 1 is 1
    The square root of 4 is 2
    The square root of 9 is 3
    The square root of 16 is 4
    The square root of 25 is 5
    ...

    Very interesting!
  2. 15 Oct '03 18:01
    Originally posted by Milou
    Do you know that:

    Sum - odd numbers
    1=1
    1+3=4
    1+3+5=9
    1+3+5+7=16
    1+3+5+7+9=25
    ....

    Square roots
    The square root of 1 is 1
    The square root of 4 is 2
    The square root of 9 is 3
    The square root of 16 is 4
    The square root of 25 is 5
    ...

    Very interesting!
    sum_odd(1..n) = average value * number of entries
    = (1 + n)/2 * (1 + n)/2
    =((1 + n)/2)^2
  3. 17 Nov '03 20:56
    2^2=4
    3^2=(2+1)(2+1)=FOIL=4+2+2+1=9
    (X+1)^2=X*X+X+X+1
    (X+1)^2=X(X+2)+1

    1+3=4
    1+3=1+1+1+1
    X=1 X+1=2 2=number of odd numbers being added
    1+3=X+X+X+1
    1+3=3X+1
    3X=1+1+1
    1+1+1=1(1+2) because X=1, 1(1+2)=X(X+2) thus
    1+3=X(X+2)+1
    1+3+5=?
    X=2 (the old X+1) X+1=3 3=the number" "added
    1+3+5=X(X+2)+1=3(3+2)+1=

    i have no idea where this is going.