Summation Σ

In mathematics, the summation, denoted $ \sum $, is the result of the addition of a series of numbers.

The symbol ∑ is called the sum operator, it is an addition calculator (finite or infinite).

In arithmetic, the summation notation $ \sum_1^n $ (with the Greek letter sigma uppercase) allows to compute a finite addition going from $ 1 $ to $ n $ with an increment of 1 (by default).

Sometimes the sum can be simplified with a formula:

The calculation by hand is time-consuming, some sums are interesting to learn/know.

The notation $ \sum_1^\infty $ (sometimes shortened in $ \sum $) indicates the computation of an infinite addition going from $ 1 $ to infinity $ \infty $ with an increment of 1 (by default).

The demonstration of these sums often involves a limit calculation or a series expansion.

The notation $ \sum \sum $ is read $ \sum \left( \sum \right) $ so the inner sum (inside the parenthesis) is calculated first first, before the outer sum is calculated in a second step.

The summation is written with the dedicated mathematical operator ∑ (Unicode U+2211) inspired from the Greek letter sigma uppercase Σ (Unicode U+03A3).

In Greek, sigma corresponds to the letter S (like the first letter of Sum).

In LaTeX, the operator is \sum