I'm studying computer science, but my maths is a little lacking, and my course material isn't being explicit about how things are calculated (they expect you to just know).
Given a sequence such as:
(n − 1) + (n − 2) + ⋯ + 1
That results in the formula (if that's even the correct term?):
½n^2 − ½n
So:
(n − 1) + (n − 2) + ⋯ + 1 = ½n^2 − ½n
How do I work out what that formula(?) is?
What is that type of maths called?
I'm at a real loss... Without having any direction, it's nearly impossible to Google for a solution.
UPDATE:
So if I only had:
(n − 1) + (n − 2) + ⋯ + 1
How would I work out what the formula would be?
Hint. You could use the following trick to obtain the formula: \begin{matrix} (n − 1) &+& (n − 2) &+& \dotsm &+& 1 \\ 1 &+& 2 &+&\dotsm &+& (n − 1) \\ \hline n &+& n &+& \dotsm &+& n \end{matrix}