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Math 71B

11.1 – Sequences and Summation Notation

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A ______________ is an ordered list.ex:

The 1, 3, 5, 7, 9, etc. are called _________. So, the fourth term in our example is _____.

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A ______________ is an ordered list.ex:

The 1, 3, 5, 7, 9, etc. are called _________. So, the fourth term in our example is _____.

sequence

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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

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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

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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

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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

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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

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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

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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

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A sequence can be finite or infinite.

ex: is ___________.

ex: is ___________.

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A sequence can be finite or infinite.

ex: is ___________.

ex: is ___________.

finite

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A sequence can be finite or infinite.

ex: is ___________.

ex: is ___________.

finite

infinite

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Rather than using , mathematicians usually use _____ for sequences (where is a natural #).

So, the terms of a sequence called are

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Rather than using , mathematicians usually use _____ for sequences (where is a natural #).

So, the terms of a sequence called are

𝒂𝒏

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Ex 1.Write the first three terms of the sequence

Ex 2.Write the first four terms of the sequence .

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__________________________________

______

Ex 3.

(Note: )

Factorial Notation

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__________________________________

______

Ex 3.

(Note: )

Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏

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__________________________________

______

Ex 3.

(Note: )

Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏

𝟏

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__________________________________

______

Ex 3.

(Note: )

Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏

𝟏

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__________________________________

______

Ex 3.

(Note: )

Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏

𝟏

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__________________________________

______

Ex 3.

(Note: )

Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏

𝟏

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__________________________________

______

Ex 3.

(Note: )

Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏

𝟏

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__________________________________

______

Ex 3.

(Note: )

Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏

𝟏

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__________________________________

______

Ex 3.

(Note: )

Factorial Notation𝒏⋅ (𝒏−𝟏 ) ⋅ (𝒏−𝟐 )⋅… ⋅𝟑 ⋅𝟐 ⋅𝟏

𝟏

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Ex 4.Write the first three terms of the sequence

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Summation Notation

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Ex 5.Expand and evaluate each sum.

Summation Notation

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Ex 6.Express each sum using summation notation.

Summation Notation

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Ex 6.Express each sum using summation notation.

Summation Notation

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Ex 6.Express each sum using summation notation.

Summation Notation

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Ex 6.Express each sum using summation notation.

Summation Notation