In german this formula is known as "Gaußsche Summenformel" because it's said that Carl Friedrich Gauß realized this when he was 9 years old.
I couldn't find much about it in english, only this: https://mathbitsnotebook.com/Algebra2/Sequences/SSGauss.html
In the 8th picture (below "What permissions do they have?") it says "owner" though it should be "other".
In german this formula is known as "Gaußsche Summenformel" because it's said that Carl Friedrich Gauß realized this when he was 9 years old.
I couldn't find much about it in english, only this:
https://mathbitsnotebook.com/Algebra2/Sequences/SSGauss.html