Tool to perform formal calculations with the summation operator Σ (sigma), allowing arithmetic additions from 1 to n.

Summation Σ - dCode

Tag(s) : Arithmetics

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Tool to perform formal calculations with the summation operator Σ (sigma), allowing arithmetic additions from 1 to n.

In mathematics, 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).

__Example:__ The sum of the first $ 5 $ integers $$ 1 + 2 + 3 + 4 + 5 = \sum_{i=1}^{5} i $$

Sometimes the sum can be simplified with a formula:

__Example:__ The sum of the $ n $ first integers $$ 1 + 2 + 3 + \cdots + (n-1) + n = \sum_{i=1}^{n} i = \frac{n(n+1)}{2} $$

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

Parfois la somme ne converge pas vers une valeur, elle peut diverger et ne pas avoir de formule permettant de la calculer.

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

__Example:__ The sum of the inverses of the $ n $ prime squares (Basel problem) $$ \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots = \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} $$

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

The **summation** is written with the Greek letter sigma uppercase Σ (Unicode U + 03A3). In Greek, sigma corresponds to the letter S (like the first letter of Sum).

The LaTeX, the operator is '\ sum'

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Source : https://www.dcode.fr/summation-calculator

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