Sigma Notation

Sigma notation (∑) provides a compact way to write the sum of a sequence of terms. The Greek capital letter sigma (∑) means "sum". This notation is used extensively in A-Level Mathematics (9MA0) and understanding it is essential for work with series.

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Key Notation

The expression ∑ from r = 1 to n of f(r) means: add up f(r) for r = 1, 2, 3, ..., n.

Component	Meaning
∑	"The sum of"
r	The index variable (also called the dummy variable)
r = 1 (below ∑)	The starting value of r
n (above ∑)	The final value of r
f(r)	The expression to be summed

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Writing Sums in Sigma Notation

Worked Example 1

Write the sum 2 + 4 + 6 + 8 + ... + 100 using sigma notation.

Each term is 2r, where r goes from 1 to 50.

∑ (r = 1 to 50) 2r

Worked Example 2

Write the sum 1 + 4 + 9 + 16 + ... + 400 using sigma notation.