SOLUTION: What would be another way to add 1+3+5+7+9+....499=to equal the sum of 62,500? Only using odd numbers. We need another way to find the sum of all the odd numbers from 1 to 499 and

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Question 15189: What would be another way to add 1+3+5+7+9+....499=to equal the sum of 62,500?
Only using odd numbers. We need another way to find the sum of all the odd numbers from 1 to 499 and equal 62,500
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
1+3+5+7+9+....499
Before you begin, notice that you are adding numbers from 1 to 499, omitting the even numbers in between, so there will be a total of 250 numbers that are added together.

Pair these numbers up by adding 1+499, 3+497, 5+495, etc.

Notice that each sum is 500, and the number of such pairs will be half of the 250 numbers that are added together, or 125. Therefore, the sum will be 500 times 125 = 62500.

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