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

Summation Σ - dCode

Tag(s) : Arithmetics

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

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'

dCode retains ownership of the online 'Summation Σ' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Summation Σ' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Summation Σ' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Summation Σ' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

Please, check our dCode Discord community for help requests!

NB: for encrypted messages, test our automatic cipher identifier!

sum,summation,sigma,index,addition,plus,power,serie

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

© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback

▲
Thanks to your feedback and relevant comments, dCode has developed the best 'Summation Σ' tool, so feel free to write! Thank you!