AP Calculus AB and BC glossary

Sigma notation

Also called: Summation notation

Sigma notation writes a sum compactly using the Greek capital sigma, with an index variable, a starting value below and a stopping value above. It is the standard way to express a Riemann sum and every infinite series in the course.

∑i=1nai=a1+a2+⋯+an\sum_{i=1}^{n} a_{i} = a_{1} + a_{2} + \cdots + a_{n}

The index is a dummy variable: renaming it from i to k changes nothing. What matters is the starting value, because shifting where the sum begins changes the answer.

The mistake

Assuming a sum starts at one. Riemann sums and power series frequently start at zero, and an off-by-one start is the most common error in the notation.

Appears in: Unit 6: Integration and Accumulation, Unit 10: Infinite Sequences and Series (BC)