Sequence : a function whose domain is the non-negative integers.

Section 1: Sequences & Serieshttps://sites.google.com/site/bchsapcalculusbc/units/unit-10-chp-11-sequences-series

Sequence: a function whose domain is the non-negative integers. • an = terms in the sequence • n = 1, 2, 3 … or 0, 1, 2…

n factorial = n! • The product of the first n natural numbers.

Ex 1: Find the first 5 terms:a)b)

Ex 2: • Give an expression for the general form of the sequence:

Limits of Sequences • If the limit, , exists then {an} converges. • If the limit DNE, then {an} diverges.

Ex 3: Does the following sequence Converge OR Diverge?

Series or Infinite Series: the sum of the terms of an infinite sequence.

Partial Sums:

Ex 4: • Find the 5th, 10th, and 25th partial sum of the series:

Limits of Series • If the sequence Sn diverges, then  an is a divergent series.

If the sequence Sn converges to a value S, then  an is a convergent series such that: If S exists, then S is the sum of the infinite series.

Properties of Sums

The nth Term Test: If then the series is DIVERGENT.

Ex 5: • Show that the following series diverges

Harmonic Series • DIVERGENT!

Section 1A WS#1 – 6 all,# 7 – 15 odds

Geometric Series • a = 1st term • r = common ratio

Sum of an Infinite Geometric Series: If |r| < 1

The Geometric Series Test:

Ex 6: • Convergent? If so, find the sum: • c) • d)

Ex 7: • Write 0.8888888… as a fraction.

Ex 8: Does the following series Converge OR Diverge?

Section 1B WS#17 – 25 odds,27 – 37 odds,40 – 44 all

Ex 9: Does the following sequence Converge OR Diverge?

Sequence : a function whose domain is the non-negative integers.