Summation Notation

Summation Notation

Introduction

• The greek letter sigma allows us to describe a range of values, and then add them all together.
• For example, if we want to add the numbers from 1 to 4, we can write:
• This expands to: 1 + 2 + 3 + 4
• The value of n starts at 1 (written under the sigma), and ends on 4 (written above the sigma).

A more complex sum

• In the introductory example, we simply put n after our sigma, however we can write more complex equations too:
• This would expand to:

Summing sets

• If we have a set of numbers, for example: S = [2, 5, 3], then we can sum it with:
• Where |S| is the length of the set, and Sn is the nth value of S.
• This is often simplified to:

LaTeX

\sum_{n = 1}^{x}

code (Python)

numbers = [1,2,3,4]

summed = sum(numbers)
print(summed) # prints 10