![]() That it exists, just so you know that induction Induction, so it wouldn't be included in that video. This video is show you that there's actually a ![]() Integers up to and including n can be expressed as n Proved that the sum of all of the positive I hope that although I couldn't answer your question, that I at least entertained you a bit with these stories. For example, it is said that Napier invented the base of the natural logarithm because he wanted to know how much money he would make if it were compounded continuously. ![]() (Many results in physics and calculus were discovered long before Newton published them) However, there are some amusing anecdotes like that Gauss story for many other results. Like many mathematical results, it is often unclear from where they originate. There are many versions of this story, and it is not very clear if it is even true. The total sum is then a very easily computable 50 * 101 = 5050. So, since you had 100 numbers, that means you had 50 pairs of numbers, that all added up to 101. Of course, Gauss noticed that if he added 1 to 100, and 2 to 99, and 3 to 98, all the sums added up to 101. His teacher wanted him to add up all the numbers from 1 to 100, thinking that it would take Gauss all afternoon. It is said that Carl Friedrich Gauss, one of the greatest mathematicians of all time, was punished by a very mean teacher. The formula for this probably dates back some one or two thousand years, but perhaps you will be interested by this amusing story:
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