Wednesday, March 9, 2011
More Odd Numbers
The sum of a sequence of odd numbers is always divisible by half of the sum of the first and last odd numbers in the sequence. For example, 7 + 9 + 11 + 13 is divisible by ½(7 + 13), and 3 + 5 + 7 + 9 + 11 is divisible by ½(3 + 11). Why?
Odd Numbers
It's been a hectic month. I am now employed again, and have had little time for word problems. However, here's a good brain teaser.
A number is "singly even" if it can be evenly divided by 2 but not by 4. The numbers 2, 6, 10, 14, 18, ... are all "singly even." Show that the sum of a sequential series of odd numbers (e. g., 9 + 11 + 13 + 15) must be odd or divisible by 4; it cannot be "singly even."
A number is "singly even" if it can be evenly divided by 2 but not by 4. The numbers 2, 6, 10, 14, 18, ... are all "singly even." Show that the sum of a sequential series of odd numbers (e. g., 9 + 11 + 13 + 15) must be odd or divisible by 4; it cannot be "singly even."
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