Question 466706: The average of all odd numbers less than 100??
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! I hope you mean "average of all odd positive numbers less than 100" because there are infinitely many odd numbers less than 100.
We can add up the numbers 1, 3, ..., 99, then divide by 50:
 + (3+97) + (5+95) + ... + (49+51)}{50})
 (there are 25 pairs of 100, simply obtained by counting the number of elements in the set {1, 3, 5, ..., 49})
So the average of all these numbers is 50. This makes sense, because 50 is halfway between 0 and 100.
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