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).

  • 3
    $\begingroup$ "Evaluating a sum" $\endgroup$
    – JMoravitz
    Dec 12, 2019 at 17:39
  • $\begingroup$ @TheDemonix_Hermit thanks. As this is a soft-question, I think you can give that as an answer in itself $\endgroup$ Dec 12, 2019 at 17:39

1 Answer 1


We generally call it the Closed Form of the expression . So $\dfrac{n(n+1)}{2}$ is the closed form of $\sum_{k=1}^n k$ .


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