Chapter 11 - Sequences and Series

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Pre-Calculus

Series

Last updated 2:25 AM on 5/17/22
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23 Terms

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Index of summation
________- the variable in sigma notation Example 2- Evaluate a Sum in Sigma Notation.
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fraction form
Let x equal the ________ of the decimal.
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Factorials
________- an operation where the factorial of a number is equal to the product of the number and its previous successive terms
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Binomial Theorem
The ________- another way to show the coefficients in a binomial expansion (they are written in terms of the previous coefficients)
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triangular formation
The coefficients are symmetric (increase in the beginning and decrease at the end) Pascals triangle- the coefficients form a pattern in a(n) ________.
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Sequence
a list of numbers in a particular order; a discrete function whose domain is the set of all positive integers over an interval
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Arithmetic sequence
a sequence where each term after the first is found by adding a constant
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Common difference
the constant added to each term
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Arithmetic means
the terms between any two nonsuccessive terms of an arithmetic sequence
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Series
an indicated sum of the terms of a sequence
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Arithmetic series
a series of the terms of an arithmetic sequence
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Geometric sequence
a sequence in which each term after the first is found by multiplying theprevious term by a nonzero constant r
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Common ratio
the nonzero constant
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Geometric means
missing term(s) between two nonsuccessive terms of a geometric sequence
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Geometric series
the sum of the numbers in a geometric sequence
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Infinite geometric series
a geometric series in which there is no last term
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Convergent series
an infinite series that has a sum
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The Fibonacci sequence
a sequence where each term is the sum of the previous two terms
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Recursive formula
a formula where each term is formed from one or more previous terms
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Iteration
the process of composing a function with itself repeatedly
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Pascal’s Triangle
the coefficients form a pattern in a triangular formation
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Factorials
an operation where the factorial of a number is equal to the product of the number and its previous successive terms
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Mathematical induction
used to prove statements about positive integers