Let's say I have the following sum:
This can obviously be replaced with Gauss's formula, which doesn't use a sum function or any inherent 'looping':
Similarly, we can do this with summing of squares:
And many more (although not all) series. Is there a name for this process of getting rid of the sum for a non-loopy formula? I was thinking 'linearisation', but that seemed too ambiguous, and misleading as it often involves squaring numbers (i.e making them less linear).