math 71b 11.1 – sequences and summation notation 1
TRANSCRIPT
1
Math 71B
11.1 – Sequences and Summation Notation
2
A ______________ is an ordered list.ex:
The 1, 3, 5, 7, 9, etc. are called _________. So, the fourth term in our example is _____.
3
A ______________ is an ordered list.ex:
The 1, 3, 5, 7, 9, etc. are called _________. So, the fourth term in our example is _____.
sequence
4
A ______________ is an ordered list.ex:
The 1, 3, 5, 7, 9, etc. are called _________. So, the fourth term in our example is _____.
sequence
terms
5
A ______________ is an ordered list.ex:
The 1, 3, 5, 7, 9, etc. are called _________. So, the fourth term in our example is _____.
sequence
terms7
6
We can think of sequences as functions that take natural #’s as input.
Input 1 to get the first term of the sequence, input 2 to get the second term, and so on…
ex: The list becomes
7
We can think of sequences as functions that take natural #’s as input.
Input 1 to get the first term of the sequence, input 2 to get the second term, and so on…
ex: The list becomes
8
We can think of sequences as functions that take natural #’s as input.
Input 1 to get the first term of the sequence, input 2 to get the second term, and so on…
ex: The list becomes
9
We can think of sequences as functions that take natural #’s as input.
Input 1 to get the first term of the sequence, input 2 to get the second term, and so on…
ex: The list becomes
10
We can think of sequences as functions that take natural #’s as input.
Input 1 to get the first term of the sequence, input 2 to get the second term, and so on…
ex: The list becomes
11
A sequence can be finite or infinite.
ex: is ___________.
ex: is ___________.
12
A sequence can be finite or infinite.
ex: is ___________.
ex: is ___________.
finite
13
A sequence can be finite or infinite.
ex: is ___________.
ex: is ___________.
finite
infinite
14
Rather than using , mathematicians usually use _____ for sequences (where is a natural #).
So, the terms of a sequence called are
15
Rather than using , mathematicians usually use _____ for sequences (where is a natural #).
So, the terms of a sequence called are
𝒂𝒏
16
Ex 1.Write the first three terms of the sequence
Ex 2.Write the first four terms of the sequence .
17
__________________________________
______
Ex 3.
(Note: )
Factorial Notation
18
__________________________________
______
Ex 3.
(Note: )
Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏
19
__________________________________
______
Ex 3.
(Note: )
Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏
𝟏
20
__________________________________
______
Ex 3.
(Note: )
Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏
𝟏
21
__________________________________
______
Ex 3.
(Note: )
Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏
𝟏
22
__________________________________
______
Ex 3.
(Note: )
Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏
𝟏
23
__________________________________
______
Ex 3.
(Note: )
Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏
𝟏
24
__________________________________
______
Ex 3.
(Note: )
Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏
𝟏
25
__________________________________
______
Ex 3.
(Note: )
Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏
𝟏
26
Ex 4.Write the first three terms of the sequence
27
Summation Notation
28
Ex 5.Expand and evaluate each sum.
Summation Notation
29
Ex 6.Express each sum using summation notation.
Summation Notation
30
Ex 6.Express each sum using summation notation.
Summation Notation
31
Ex 6.Express each sum using summation notation.
Summation Notation
32
Ex 6.Express each sum using summation notation.
Summation Notation