Answer by Pradeep Bansal:

Late 1700s, in a German elementary school, as a punishment for misbehaving with the teacher, he was asked to sum 1 to 100.
The teacher was astonished when a kid solved this within seconds as:

S = 1 + 2 + …….+ 100
S= 100 + 99 +….+ 1
———————————
2S = 101 + 101 + ….+ 101 (100 times)
     = 101×100

=> S = 101×100/2 = 5050

The student was the famous mathematician and physical scientist Carl Friedrich Gauss.

What is the most beautiful theorem proof, and why?

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