TeXipedia

sum

Represents summation in mathematical expressions, indicating the addition of a sequence of terms.

Overview

Essential for expressing finite and infinite series across mathematics and related disciplines, particularly in sequences, statistics, and computational formulas.

  • Commonly paired with subscripts and superscripts to define iteration bounds
  • Fundamental in discrete mathematics and numerical analysis
  • Frequently used in probability theory for expected values
  • Appears extensively in scientific computing and algorithmic complexity notation

Examples

Sum of first n integers using standard summation notation

∑i=1ni=n(n+1)2\sum_{i=1}^{n} i = \frac{n(n+1)}{2} 
\sum_{i=1}^{n} i = \frac{n(n+1)}{2}

Double summation for matrix elements with subscripts

∑i=1m∑j=1naij\sum_{i=1}^{m} \sum_{j=1}^{n} a_{ij} 
\sum_{i=1}^{m} \sum_{j=1}^{n} a_{ij}

Infinite series representation of e^x

ex=∑n=0∞xnn!e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} 
e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}