Sigma Notation

Sigma Notation

## Definition / Concept

Sigma notation represents the sum of a sequence compactly.

## Formula

$$\sum_{k=m}^{n}a_k=a_m+a_{m+1}+\cdots+a_n$$

## Properties

$$\sum_{k=1}^{n}(a_k+b_k)=\sum_{k=1}^{n}a_k+\sum_{k=1}^{n}b_k$$

$$\sum_{k=1}^{n}(a_k-b_k)=\sum_{k=1}^{n}a_k-\sum_{k=1}^{n}b_k$$

$$\sum_{k=1}^{n}ca_k=c\sum_{k=1}^{n}a_k$$

## Usage

- Used to represent and manipulate finite sums efficiently.