Section 1: Sequences & Series /units/unit-10-chp-11-sequences-series /units/unit-10-chp-11-sequences-series

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

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

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

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

Limits of Sequences If the limit,, exists then {a n } converges. If the limit DNE, then {a n } diverges.

Ex 3: Does the following sequence Converge OR Diverge?

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

Partial Sums: Partial Sums:

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

Limits of Series If the sequence S n diverges, then  a n is a divergent series.

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

Properties of Sums Properties of Sums 1) 1)

Properties of Sums Properties of Sums 2) 2)

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

Show that the following series diverges Show that the following series diverges Ex 5:

Harmonic Series DIVERGENT!

Section 1A WS #1 – 6 all, # 7 – 15 odds

Geometric Series a = 1 st term r = common ratio

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

The Geometric Series Test:

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

Write … as a fraction. Write … as a fraction. Ex 7:

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?