Math Playground
Algebra

Sigma notation

∑ — the compact way to write a long sum.

∑ is shorthand for 'sum'. Below: starting index. Above: ending index. Inside: the term to sum.

Try this
4
Σ i² from i=1 to n = 1² + 2² + … + n² = 30

Reading a Σ

  • Below Σ: the index variable and where it starts (e.g. i = 1).
  • Above Σ: where the index stops.
  • To the right of Σ: the term — a formula in the index. Plug in each value and add them up.
Handy closed forms

These let you collapse a sum into a single expression — no looping required.

Your turn

Evaluate Σ (2k + 1) for k = 2 to 5.

Try it

∑ᵢ₌₁⁴ i² = ?

1 + 4 + 9 + 16 = 30.