# Gauss's Trick - Arithmetic Sums

by Johnathanrs
Tags: arithmetic, gauss, sums, trick
 P: 1 I can't grasp the underlying process on how this is working. n/2(f+l) = algorithm sum of all integers n= number of all integers f= first integer l= last integer Example: 1, 2, 3, 4 4/2(1+4) 2(5) = 10 I know how to do it, but I don't really understand how to actually do it. Am I just too stupid? Why do I need to split the sum of all integers? Why am I adding the first + last integer? Why when I times them together does it work? How did he create the algorithm for this?
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 6,331 In order to see how this works, write down the string of integers in two different ways:  1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 What do you notice about the sum of each column of numbers?
 Engineering Sci Advisor HW Helper Thanks P: 6,959 What Gauss did (according to the usual story) was to pair off the numbers like this. Suppose you want to sum the 9 numbers 7 8 9 10 11 12 13 14 15 7 + 15 = 22 8 + 14 = 22 9 + 13 = 22 10 + 12 = 22 11 = 22/2 So the sum = (9/2)(22) = (9/2)(7+15)

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