Math 71B 11.1 – Sequences and Summation Notation 1.

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