You can use the Greek capital letter sigma,
For example, you can write the series
For an infinite series, summation notation shows
To find the number of terms in a series written in
The number of terms in the series above is
Problem 3 Writing a Series in Summation Notation
Multiple Choice What is summation notation for the series?
Plan
What do you need to write a series in summation notation?
You need an explicit formula for the nth term and the lower and upper limits.
The sequence 7, 11, 15, …, 203, 207 is arithmetic with first term
An explicit formula for the nth term is
The upper limit is 51. You can write the series as
✓ Got It?
- What is summation notation for the series?
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Take Note Key Concept: Summation Notation and Linear Functions
If the explicit formula for the nth term in summation notation is a linear function of n, then the series is arithmetic. The slope of the linear function is the common difference between terms of the series.
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions