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Summation Σ

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

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Summation Σ -

Tag(s) : Arithmetics

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# Summation Σ

## Sum Σ Calculator

### How to calculate a finite sum?

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.

### How to calculate an infinie de sum?

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.

### How to make the Σ sum symbol?

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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