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Set Q is defined as odd integers from 1 to 2000. How many ordered pairs (a,b) are there in set Q whereby a<b?

  • Math -

    for any odd number (b), there are (b-1)/2 odd numbers less than it.

    check on that thinking. for b= 11, the odd numbers less are 1,3,5,7,9 or five. Yep, it works.

    There are 1000 numbers for the choice of b, so there must be this number of ordered pairs:

    Sum b=1 to 1999(0dd) of (b-1)/2

    Sum 1/2 (b-1)= 1/2 sum b - 1/2 sum
    and see if you can sum those from 1 to 1999

  • Math -

    Thanks for responding, it really helped.

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