Summation Formulas

Summation notation, written with the sigma symbol Σ, provides a compact way to add a sequence of terms. Common summation formulas make it possible to evaluate long series efficiently.

Sum of the First n Integers

Σk from 1 to n = n(n + 1) ÷ 2

Sum of Squares

Σk² from 1 to n = n(n + 1)(2n + 1) ÷ 6

Sum of Cubes

Σk³ from 1 to n = [n(n + 1) ÷ 2]²

Arithmetic Sequence

The sum of the first n terms of an arithmetic sequence is Sₙ = n(a₁ + aₙ) ÷ 2, where a₁ is the first term and aₙ is the nth term.

Using Summation Notation

Identify the starting value, ending value, and expression being added. Then select the appropriate formula or expand the terms when a standard identity does not apply.