Problema Solution
The famous mathematician Carl Friedrich Gauss solved this as a grade-school student. The story goes that when Carl Friedrich Gauss was a grade student the class was acting up and the teacher told the students to take out their pencils and paper and total the numbers from 1 to 100. Well, the students were quickly adding the numbers up except for Carl Friedrich Gauss. He sat there, thought about it for a couple of minutes, then did one addition and one multiplication and handed in a number to the teacher. The teacher looked at him and thought, "You can't be serious!" Little did she know he was and that he would become one of the greatest Mathematicians the world has ever known.
Total the numbers from 1 to 100.
Answer provided by our tutors
we need to calcite
1 + 2 + 3 + 4 + … + 98 + 99 + 100 = ?
if we split the numbers into two groups (1 to 50 and 51 to 100), we could add them together vertically to get a sum of 101:
1 + 2 + 3 + 4 + 5 + … + 48 + 49 + 50+
100 + 99 + 98 + 97 + 96 + … + 53 + 52 + 51=
= (1 + 100) + (2 + 99) + (3 + 98) + ... + (50 + 51) =
= 50*(1 + 100) = 50*101 = 5050 that is
1 + 2 + 3 + 4 + … + 98 + 99 + 100 = 5050