What are the rules of sigma notation?

Sigma notation (∑) is a mathematical shorthand used to represent the sum of a series of numbers. It uses the Greek letter sigma (∑) which stands for "sum".

Let’s break down the rules in a simple and clear way:
General Format:

Σ(i = a to b) f(i)

Where:

• Σ = Sigma symbol (means "sum up")
• i = index of summation (can be any letter, commonly i, j, or k)
• a = lower limit (starting value)
• b = upper limit (ending value)
• f(i) = the expression being summed (could be any formula or term)

Rules of Sigma Notation:

1. Start from the Lower Limit - Begin with the value of the index given at the bottom of the sigma symbol (e.g., i = 1).
2. End at the Upper Limit - Continue summing until the index reaches the value at the top of the sigma (e.g., i = 5).
3. Plug in the Values - For each step, plug the current index value into the expression f(i) and compute the result.
4. Add All Results Together  - Add up all the calculated values from each step to get the final answer.

Quick Tips:

• Factor out constants: Σ(i=1 to n) 3i = 3 Σ(i=1 to n) i
• Split sums: Σ(i=1 to n) (i + 2) = Σ(i=1 to n) i + Σ(i=1 to n) 2

Rules of Sigma Notation Summary: