Sum formula of 1 and arithmetic progression

/kloc-at the age of 0/0, Gauss, the "prince of mathematics", entered the first class for studying mathematics. Children have never heard of such a course as arithmetic before. Math teacher Butner gave a question,

1+2+3 ... How much is this from 1 to 100?

Gauss quickly worked out the answer. At first, Mr. Butner didn't believe it and said, "You must have miscalculated. Go back and do it again. "

Gauss said the answer is 5050, because1+100 =1,2+99 =101...1add up to/kloc-0.

2. Limit-Tortoise and Rabbit Paradox

This primary and middle school student can't understand it. If you are interested, you can look at the introduction of Baidu Encyclopedia.