Practice Sigma Notation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Sigma notation uses the Greek letter ฮฃ to express the sum of many terms compactly. The expression \sum_{i=1}^{n} a_i means 'add up a_i for every integer i from 1 to n.' For example, \sum_{i=1}^{4} i^2 = 1 + 4 + 9 + 16 = 30.
Sigma notation is shorthand for 'add these all up.' The letter below \Sigma is a counter, the number below is where to start, the number above is where to stop, and the expression to the right tells you what to add each time.
Example 1
easyExpand and evaluate \displaystyle\sum_{k=1}^{5} (2k - 1).
Example 2
mediumWrite 1^2 + 2^2 + 3^2 + \cdots + n^2 in sigma notation and evaluate the closed form for n = 10.
Example 3
easyEvaluate \displaystyle\sum_{i=0}^{4} 3^i.
Example 4
mediumRewrite \displaystyle\sum_{j=1}^{n}(3j^2 + 2j - 1) using linearity of summation.