At a young age, Gauss shocked his teacher by finding the sum of the first $100$ positive integers quickly using the formula $$1+2+\cdots+n=\frac{n(n+1)}{2}.$$ We use a generalization of his techique to find the sum of an arithmetic series.
At a young age, Gauss shocked his teacher by finding the sum of the first $100$ positive integers quickly using the formula $$1+2+\cdots+n=\frac{n(n+1)}{2}.$$ We use a generalization of his techique to find the sum of an arithmetic series.