A formula young
Gauss discovered when trying to add the numbers 1-100, which goes n(n+1)/2, which is (100*101)/2, or 5050. He found it by discovering that 100+1=101, 99+2=101, 3+98=101...50+51=101. He found out that by wrapping the numbers around, that is adding (100-1) and (1-100) together, he would get the number 100 at every
term. He then multiplied 100 times the number of terms, and got his answer, when dividing it by 2, because he had added twice the
sum he wanted. Hence the sum of all integers between 1 and 100 is 101*50=5050.
{Editorial note: Thanks to whizkid for helping to correct the errors originally in this node.}