Title: Math 30 College Algebra May 1, 2000
1Math 30 --- College AlgebraMay 1, 2000
- Section 6.1 due
- Section 6.2 and 6.3 questions
- Break
- Section 6.4
- Assignments 32
2AnnouncementsMay 1, 2000
- Final Wednesday May 17, 3 pm
- Exams Returned Wednesday
3Arithmetic Sequences
A sequence is arithmetic if there exists a number
d, called the common difference, such that
The nth term of an arithmetic sequence is given by
4Sum of First n Terms of an Arithmetic Sequence
The sum of the first n terms of an arithmetic
sequence is
5Geometric Sequence
A sequence is geometric if there exists a number
r, called the common ratio, such that
The nth term of an arithmetic sequence is given by
6Sum of First n Terms of an Geometric Sequence
The sum of the first n terms of a geometric
sequence is
7Limit or Sum an Infinite Geometric Series
When , the limit or sum of an inifinte
geometric series is given by
8Combinatorics
The theory of counting is called
combinatorics. Two branches of combinatorics 1)
Permutations Order is important. 2)
Combinations Order is not important.
9Fundamental Counting Principle
Given a combined action, or event, in which the
first action can be performed in ways, the
second action can be performed in ways, and
so on, the total number of ways in which the
combined action can be performed is the product
10Permutation
A permutation of a set of n objects is an ordered
arrangement of all n objects. The total number
of permutations of n objects, denoted is given
by where is n factorial.
11Factorials
n factorial, denoted is given by We define
Notice that for any natural number n,
12Permutation of n Objects Taken k at a Time
A permutation of a set of n objects taken k at a
time is an ordered arrangement of k objects taken
from the set.
13Permutation of n Objects Taken k at a Time
The number of permutations of n objects taken k
at a time, denoted is given by
14Assignment 32
- 6.5 pbs 1--29 (odd), 33, 39, 41, 43, 45, 46, 49