Actually, this is very simple. It is a formula of sorts that I dreamed up 30+ years ago in high school. It applies to adding consecutive numbers (there is no known reason to add consecutive numbers, but that didn't stop my wandering mind from coming up with this scheme). Say for instance, you want to add the numbers 1 through 10, i.e., 1+2+3+4+5+6+7+8+9+10=?

Here's how.

First half of numbers 1 2 3 4 5
Second half of numbers in reverse order 10 9 8 7 6
Sum of first and second half numbers 11 11 11 11 11

Are you with me? What you have is 5 columns that add up to 11, so the sum total of the numbers 1 through 10 is 55 (11x5).

The same princple applies to the numbers 1 through 100, or 1 through any number. Here is a condensed example of 1 through 100.

First half of numbers 1 2 3 4 5 6 7 8 ... 50
Second half of numbers in reverse order 100 99 98 97 96 95 94 93 ... 51
Sum of first and second half numbers 101 101 101 101 101 101 101 101 ... 101

What you have is 50 columns that add up to 101, so the sum total of the numbers 1 through 100 is 5,050 (101x50).

Now, I'm sure you know this site is copyrighted, so don't steal this potential Nobel Prize for mathematics. But, if you find a practical application, I'll share it with you.

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