What sigma means
Big idea: Sigma notation is a short way of writing a sum.
It tells you what to add, where to start, and where to stop.
How to read it
Read each part of the sigma separately.
Bottom
The bottom tells you where to start.
Start at 1.
Top
The top tells you where to stop.
Stop at 4.
Expression
The expression on the right tells you what to add.
Add 2n + 1 each time.
Worked example
Expand this sigma notation.
Step by step
- List the values of n from 1 to 4: n = 1, 2, 3, 4.
- Substitute each value into the expression 2n + 1.
- Work out each term.
- Add the terms.
Final answer
So the value of the sum is 24.
Exam Tips:
- Read the bottom first.
- Then read the top.
- Then look at the expression on the right.
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How to read sigma
Big idea: Sigma notation tells you what to add, where to start, and where to stop.
Read it step by step
- The bottom tells you where to start.
- The top tells you where to stop.
- The expression on the right tells you what to add.
Worked example
Expand this sigma notation.
Step by step
- Use n = 1, 2, 3, 4.
- Substitute each value into 2n.
- Simplify the terms.
Final answer
So it means add 2 + 4 + 6 + 8 = 20.
Exam Tips:
- Start at the bottom number.
- Stop at the top number.
- Substitute each value of n carefully.
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How to evaluate sigma
Big idea: Sometimes sigma does not start at 1.
When the lower value is 3, you start at n = 3 and keep going until the top value.
Worked example
Evaluate this sum.
Step by step
- List the values of n from 3 to 5: n = 3, 4, 5.
- Substitute each value into the expression 2n.
- Work out each term.
- Add the terms.
Final answer
So the value of the sum is 24.
Exam Tips:
- Do not assume sigma always starts at 1.
- Read the bottom number carefully before listing the values of n.
- The values of n must include both the start and the end.