So recently I derived a formula (obviously not the first... it already existed but that is what got me into summations) that quickly adds all the numbers from 1 to "n" However I recently derived another formula (also not the first I am guessing) that adds all the numbers from any number (not just 1) to "n" (i.e. 14+15+16+17)
Where i= Starting number and n= Ending number
$$\sum_{i}^{n} = \left ( n-i+1 \right )\ast \left ( \left ( n+i \right )/2 \right )$$
What I want to know is what is this formula called? Mine is very complicated looking as well so is there a more compact way?
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