Barrons AP Calculus

B1. Definitions

Infinite    series

If an is a sequence of real numbers, then an infinite series is an expression of the

form

The elements in the sum are called terms; an is the nth or general term of the
series.

Example 7 __

p-series

A series of the form is called a p-series.

The p-series for p = 2 is .

BC  ONLY

Example 8 __

Harmonic    series

The p-series with p = 1 is called the harmonic series:

Example 9 __

Geometric   series

A geometric series has a first term, a, and common ratio of terms, r:

Convergent

If  there   is  a   finite  number  S   such    that