Answers: Introduction to sigma notation
These are the answers to Questions: Introduction to sigma notation.
Please attempt the questions before reading these answers!
Q1
1.1. \(\displaystyle \quad\sum_{i = 1}^{10} 2i = 110\)
1.2. \(\displaystyle \quad\sum_{i = 2}^{11} i = 65\)
1.3. \(\displaystyle \quad\sum_{i = 3}^{6} 3i = 54\)
1.4. \(\displaystyle \quad\sum_{i = 1}^{5} i^3 = 225\)
1.5. \(\displaystyle \quad\sum_{i = 2}^{6} 5i^2 = 455\)
1.6. \(\displaystyle \quad\sum_{i = 3}^{6} 2 = 8\)
1.7. \(\displaystyle \quad\sum_{i = 1}^{6} j = 6j\)
Q2
2.1. \(\quad 3 + 6 + 9 + 12 = \displaystyle\sum_{i=1}^43i\)
2.2. \(\quad - 1 - 2 - 3 - 4 = \displaystyle\sum_{i=1}^4-i\)
2.3. \(\quad 0 + 3 + 9 + 27 + 81 = \displaystyle\sum_{i=0}^43^i\)
2.4. \(\quad 1 + 1 + 1 + 1 + 1 = \displaystyle\sum_{i=1}^51\)
2.5. \(\quad 6 - 12 + 18 - 24 = \displaystyle\sum_{i=1}^4(-1)^{i+1}6i\)
2.6. \(\quad 8 + 16 + 12 + 4 = \displaystyle\sum_{i=1}^44i\)
2.7. \(\quad 25 + 20 + 15 + 10 + 5 = \displaystyle\sum_{i=1}^55i\)
Q3
3.1. \(\displaystyle\quad \sum_{i = 1}^{n} 2i = 2\sum_{i=1}^ni\)
3.2. \(\displaystyle\quad \sum_{i = 1}^{n} 2i + \sum_{j = 1}^{n} 2i = 4\sum_{i=1}^ni\)
3.3. \(\displaystyle\quad \sum_{i = 0}^{n} 4i + \sum_{i = 1}^{n} 2i = 6\sum_{i=1}^ni\)
3.4. \(\displaystyle\quad \sum_{i = 2}^{n} 2i - \sum_{i = 1}^{n} i = -1 + \sum_{i=2}^n i\)
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.