Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
Summation notation, often represented by the Greek letter sigma ($\Sigma$), is a concise way to express the sum of a sequence of numbers. It is commonly used to approximate areas under curves and in various mathematical analyses.
5 Must Know Facts For Your Next Test
Summation notation uses an index variable (usually $i$, $j$, or $k$) that runs from a lower bound to an upper bound.
The general form is $\sum_{i=a}^{b} f(i)$, where $a$ is the lower limit, $b$ is the upper limit, and $f(i)$ is the function being summed.
In calculus, summation notation can be used to represent Riemann sums which approximate integrals.
Summation properties include linearity: $\sum_{i=1}^{n} (a_i + b_i) = \sum_{i=1}^{n} a_i + \sum_{i=1}^{n} b_i$ and constant multiplication: $\sum_{i=1}^{n} c \cdot a_i = c \cdot \sum_{i=1}^{n} a_i$.
It is important for understanding definite integrals in Calculus II as they are the limits of Riemann sums.