Questions: Introduction to sigma notation
Before attempting these questions, it is highly recommended that you read Guide: Introduction to sigma notation.
Q1
Calculate the value of the following sums in sigma notation. You may use the properties of sums but they should not be necessary.
1.1. \(\displaystyle\quad \sum_{i = 1}^{10} 2i\)
1.2. \(\displaystyle\quad \sum_{i = 2}^{11} i\)
1.3. \(\displaystyle\quad \sum_{i = 3}^{6} 3i\)
1.4. \(\displaystyle\quad \sum_{i = 1}^{5} i^3\)
1.5. \(\displaystyle\quad \sum_{i = 2}^{6} 5i^2\)
1.6. \(\displaystyle\quad \sum_{i = 3}^{6} 2\)
1.7. \(\displaystyle\quad \sum_{i = 1}^{6} j\)
Q2
Express the following using sigma notation. Note that there are multiple correct answers for some of the questions. It is recommended to use \(i\) as your variable so that your answers will align with those provided.
2.1. \(\quad 3 + 6 + 9 + 12\)
2.2. \(\quad - 1 - 2 - 3 - 4\)
2.3. \(\quad 0 + 3 + 9 + 27 + 81\)
2.4. \(\quad 1 + 1 + 1 + 1 + 1\)
2.5. \(\quad 6 - 12 + 18 - 24\)
2.6. \(\quad 8 + 16 + 12 + 4\)
2.7. \(\quad 25 + 20 + 15 + 10 + 5\)
Q3
Using the properties listed in the guide write the following sums in their simplest form; that is, with as little information as possible within the summation.
3.1. \(\displaystyle\quad \sum_{i = 1}^{n} 2i\)
3.2. \(\displaystyle\quad \sum_{i = 1}^{n} 2i + \sum_{j = 1}^{n} 2i\)
3.3. \(\displaystyle\quad \sum_{i = 0}^{n} 4i + \sum_{i = 1}^{n} 2i\)
3.4. \(\displaystyle\quad \sum_{i = 2}^{n} 2i - \sum_{i = 1}^{n} i\)
After attempting the questions above, please click this link to find the answers.
Version history and licensing
v1.0: initial version created 08/23 by Ifan Howells-Baines, Mark Toner as part of a University of St Andrews STEP project.
- v1.1: edited 05/24 by tdhc.