From one to one hundred

Gauss has many interesting stories, and the first-hand information of these stories often comes from Gauss himself, because he always likes to talk about his childhood in his later years. We may doubt the truth of these stories, but many people have confirmed what he said.

Gauss's father works as a foreman in a tile factory. He always pays his workers every Saturday. When Gauss was three years old in the summer, when he was about to get paid, Little Gauss stood up and said, "Dad, you are mistaken." Then he said another number. It turned out that three-year-old Gauss was lying on the floor, secretly following his father to calculate who to pay. The results of recalculation proved that little Gauss was right, which made the adults standing there dumbfounded.

Gauss often joked that he had learned to calculate before he learned to speak, and often said that he learned to read by himself only after consulting adults about the pronunciation of letters.

At the age of seven, Goss entered St. Catherine's Primary School. When I was about ten years old, my teacher had a difficult problem in arithmetic class: "Write down the integers from 1 to 100 and add them up! Whenever there is an exam, they have this habit: the first person who finishes it puts the slate face down on the teacher's desk, and the second person puts the slate on the first slate, thus falling one by one. Of course, this question is not difficult for people who have studied arithmetic progression, but these children are just beginning to learn arithmetic! The teacher thinks he can have a rest. But he was wrong, because in less than a few seconds, Gauss had put the slate on the lecture table and said, "Here's the answer! Other students added up the numbers one by one, sweating on their foreheads, but Gauss sat quietly, ignoring the contemptuous and suspicious eyes cast by the teacher. After the exam, the teacher checked the slate one by one. Most of them were wrong, so the students were whipped. Finally, Gauss's slate was turned over and there was only one number on it: 5050 (needless to say, this is the correct answer. The teacher was taken aback, and Gauss explained how he found the answer:1+100 =1,2+99 =10/,3+98 =/kloc-. A * * * has 50 pairs, and the sum is 10 1, so the answer is 50 × 10 1 = 5050. It can be seen that Gauss found the symmetry of arithmetic progression, and then put the numbers together in pairs, just like the general arithmetic progression summation process.