Summation notation

Definition

Summation notation is a mathematical symbol used to represent the sum of a sequence of terms. It is denoted by the capital Greek letter sigma ($\sum$) followed by an expression that defines the terms to be added.

5 Must Know Facts For Your Next Test

1. The expression $\sum_{i=1}^{n} a_i$ represents the sum of terms $a_1, a_2, ..., a_n$.
2. The lower limit of summation (usually written under the sigma) indicates where to start summing, and the upper limit (written above the sigma) indicates where to stop.
3. Summation notation is commonly used in calculus to approximate areas under curves using Riemann sums.
4. In integration, partitioning an interval and approximating area via summation can lead to the concept of definite integrals.
5. Changing indices or limits in summation may require adjustments in the formula but does not change the overall sum.

Review Questions

• What does $\sum_{i=1}^{n} i^2$ represent?
• How would you write the sum of terms $a_3 + a_4 + ... + a_{10}$ using summation notation?
• Explain how summation notation is used to approximate areas under curves.

Related terms

Riemann Sum: A method for approximating the total area underneath a curve on a graph, otherwise known as an integral. It sums up rectangular sections under or overestimated against that curve.

Definite Integral: The evaluation of an integral within specified bounds; it provides the net area between the function and x-axis over an interval.

$\Delta x$: $\Delta x$ represents a small change or partition width in x-values, often used in defining Riemann sums and approximations.