Sigma notation

Math

Definition

A compact way to write the sum of a sequence of terms using the Greek letter Σ (sigma). It specifies a formula for each term, a starting index, and an ending index. For example, Σ from i=1 to n of aᵢ means a₁ + a₂ + ... + aₙ.

Examples

  • Σ from i=1 to 5 of i = 1 + 2 + 3 + 4 + 5 = 15
  • Σ from k=1 to 4 of k² = 1 + 4 + 9 + 16 = 30
  • Writing Riemann sums in compact form using sigma notation
Key Fact

Σ from i=1 to n of i = n(n+1)/2

Related Terms

Arithmetic sequences Geometric sequences Riemann sums

Study This Concept

Practice sigma notation with free review games in these units:

Algebra 2 Unit 8: Sequences and Series