Transcript Section 12-4 Convergent and Divergent Series

Section 11-1
Sequences and Series
Definitions
A sequence is a set of numbers in a specific
order
2, 7, 12, …
Definitions
An arithmetic sequence is a sequence in
which each term is equal to the sum of
the preceding term and the common
difference.
a1 , a1  d a1  2 d a1  3d ...

Definitions
The difference between successive terms of
an arithmetic sequence is a constant
called the common difference d

1. What is the common difference?
3
6
9
12
15
18
...
2. Find the next three terms for the
sequence 12 ,  1, 10 ...

3. Find the next three terms for the
sequence
r  4, r  1, r  2 ...

Definitions
An arithmetic series is the sum of the terms
of an arithmetic sequence.
Definitions
A geometric sequence is one in which each
term after the first is a product of the
proceeding term and a common ratio r.
a,

ar ,
2
ar ...
ar
n
5. What is the common ratio for
13, 91, 637 ?
Definitions

Limit of a function at infinity

The limit of a function is the limit as x
approaches positive or negative infinity.
It means that x either grows without bound
positively (positive infinity) or grows without
bound negatively (negative infinity).

Definitions
A sequence or series that is getting
infinitely large is said to diverge.
Definitions
A sequence or series that is getting
infinitely small is said to converge.
Definitions
The nth term is a general formula for the
sum of the terms of a sequence or series
6. Find the limit of the sequence then
determine if it converges or diverges
7
3
,
20
24
,
45
81
n  6n
3
,
...
3n
3
7.
lim
4n  6
n 
3n
2
8. Write 0.4545… as a fraction
9. Write 7.259259… as a fraction
Assignment
Practice 11-1