Practice Sigma Notation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A compact way to write the sum of many terms using the Greek letter \Sigma (sigma). \sum_{i=m}^{n} a_i means add up a_i for every integer i from m to n.

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

easy
Expand and evaluate \displaystyle\sum_{k=1}^{5} (2k - 1).

Example 2

medium
Write 1^2 + 2^2 + 3^2 + \cdots + n^2 in sigma notation and evaluate the closed form for n = 10.

Example 3

easy
Evaluate \displaystyle\sum_{i=0}^{4} 3^i.

Example 4

medium
Rewrite \displaystyle\sum_{j=1}^{n}(3j^2 + 2j - 1) using linearity of summation.