The summation represented by Sigma ($\sum$) is essentially a repetition of addition. It may look complicated, but there’s nothing intimidating once you get used to it.

シグマ ($∑$) で表される総和は要は足し算の繰り返しです。複雑に見えますが、慣れてしまえば難しいことは何もありません。

${\displaystyle {\begin{aligned}\sum _{x=1}^{10}x \end{aligned}}}$

This represents the sum of $x$ as it increments from 1 to 10, or in other words, the sum of integers from 1 to 10.


The notation with $\sum$ (Sigma) has two main components: the upper and lower limits. The lower limit below the sigma indicates the starting value, while the upper limit above is the ending value. To calculate this, start with the lower limit's value and increment it until you reach the upper limit, summing the values as you go.


It is usually written in code using a For loop, which makes it easier to understand. For example, the expression above can be written as:

コードで書く場合は大抵 For 文だと思うとわかりやすいでしょう。例えば上の式は下のように書けます。

let sum = 0;
for (let x = 1; x <= 10; x ++) { sum += x; }

Can you guess what the expression below means?


${\displaystyle {\begin{aligned}\frac {\sum _{x=1}^{n}x} n \end{aligned}}}$