Original E-mailSorry about that last e-mail but i found the answer. I looked under biography and it was there. well if you have time or don't mind explaining sum = n (n=1)/2 I would greatly appreciate it. Thanks, Julie Response: Dear Julie, Hmmm... I really hope you don't think I hug my computer all day long, as I know that this is a really fast reply. I've already written 6 Gauss-related e-mails today, so I guess one more can't hurt. Okay, you're not the only one that has asked me this, so I guess I should dedicate a section of my page to this. Okay, first off, it's: sum = n * (n+1)/2 In the parenthesis, it's n PLUS 1, not equals. I'll walk this equation through with you. Variables: Sum: the sum of all the numbers added together. N: The NUMBER of numbers. In the situation where Gauss did this problem, it was the result if one added the numbers 1 through 100 together. So, you want to find out what "sum" is. "N" is 100, since there are a hundred numbers. So, this is how it would look: Sum = N * (N+1)/2 Since N=100, replace "N"'s with the number 100: Sum = 100 * (100+1)/2 Solve for (100+1), which equals 101, which makes the equation: Sum = 100 * 101/2 Solve for 101/2, which is 50.5: Sum = 100 * 50.5 Multiply 100 and 50.5, which is 5050: Sum = 5050 And there! You got your answer! Pretty much the trick to this is that in a sequence there is a pair that makes the same sum. All one needs to do is find out how many pairs are there and what that paired up sum is. In this case of 1 to 100, there are 50 pairs. For example: 1 + 100 = 101 2 + 99 = 101 3 + 98 = 101 . . . 50 + 51 = 101 ETC. This shows that the sum is 101. And since there are 50 pairs, just add them up together: 101 * 50 = 5050 The same answer as above. However, the one above is a simple one step formula, whereas this requires several steps. Okay, I'm sure this gives you more than enough imformation that you wanted! Sincerely, Nelly "Nez" Cung Response Dear Nelly, Thank you so much!! That really helped me understand the problem and the answer better! Well I can't thank you enough! Sincerely, Julie
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