Math 71B 11.1 – Sequences and Summation Notation 1.
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Transcript of Math 71B 11.1 – Sequences and Summation Notation 1.
1
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