Barrons AP Calculus

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10 Sequences and Series

BC  ONLY

CONCEPTS    AND SKILLS

In  this    chapter,    we  review  infinite    series  for BC  Calculus    students.   Topics

include

tests   for determining convergence or  divergence,

functions   defined as  power   series,

Maclaurin   and Taylor  series,

and estimates   of  errors.

A. SEQUENCES OF REAL NUMBERS‡

An infinite sequence is a function whose domain is the set of positive integers,
and is often denoted simply by an. The sequence defined, for example, by

is the set of numbers , , . . . , . . . . The elements in this set are called the
terms of the sequence, and the nth or general term of this sequence is .
A sequence an converges to a finite number does not have a
(finite) limit, we say the sequence is divergent.

Example 1 __

Does the sequence converge or diverge?

SOLUTION: ; hence the sequence converges to 0.

Example 2 __