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- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/06%3A_Functions/6.02%3A_More_about_FunctionsWe have also seen various ways to represent functions. We have also seen that sometimes it is more convenient to give a verbal description of the rule for a function. In cases where the domain and cod...We have also seen various ways to represent functions. We have also seen that sometimes it is more convenient to give a verbal description of the rule for a function. In cases where the domain and codomain are small, finite sets, we used an arrow diagram to convey information about how inputs and outputs are associated without explicitly stating a rule. In this section, we will study some types of functions, some of which we may not have encountered in previous mathematics courses.
- https://math.libretexts.org/Courses/Community_College_of_Denver/MAT_2420_Calculus_II/05%3A_Sequences_and_Series/5.01%3A_SequencesIn this section, we introduce sequences and define what it means for a sequence to converge or diverge. We show how to find limits of sequences that converge, often by using the properties of limits f...In this section, we introduce sequences and define what it means for a sequence to converge or diverge. We show how to find limits of sequences that converge, often by using the properties of limits for functions discussed earlier. We close this section with the Monotone Convergence Theorem, a tool we can use to prove that certain types of sequences converge.
- https://math.libretexts.org/Courses/Reedley_College/College_Algebra_1e_(OpenStax)/09%3A_Sequences_Probability_and_Counting_Theory/9.01%3A_Sequences_and_Their_NotationsOne way to describe an ordered list of numbers is as a sequence. A sequence is a function whose domain is a subset of the counting numbers. Listing all of the terms for a sequence can be cumbersome. F...One way to describe an ordered list of numbers is as a sequence. A sequence is a function whose domain is a subset of the counting numbers. Listing all of the terms for a sequence can be cumbersome. For example, finding the number of hits on the website at the end of the month would require listing out as many as 31 terms. A more efficient way to determine a specific term is by writing a formula to define the sequence.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus_II__Integral_Calculus_._Lockman_Spring_2024/04%3A_Sequences_and_Series/4.01%3A_SequencesThis section introduces sequences, defining them as ordered lists of numbers generated by functions with natural numbers as inputs. It covers various types of sequences, including arithmetic and geome...This section introduces sequences, defining them as ordered lists of numbers generated by functions with natural numbers as inputs. It covers various types of sequences, including arithmetic and geometric, and explains how to represent sequences explicitly and recursively. The section also discusses limits of sequences and provides examples to illustrate how sequences behave, helping readers understand convergence and divergence.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/09%3A_Sequences_and_Series/9.01%3A_SequencesIn this section, we introduce sequences and define what it means for a sequence to converge or diverge. We show how to find limits of sequences that converge, often by using the properties of limits f...In this section, we introduce sequences and define what it means for a sequence to converge or diverge. We show how to find limits of sequences that converge, often by using the properties of limits for functions discussed earlier. We close this section with the Monotone Convergence Theorem, a tool we can use to prove that certain types of sequences converge.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_401%3A_Calculus_II_-_Integral_Calculus/03%3A_Sequences_and_Series/3.02%3A_SequencesThis section introduces sequences, defining them as ordered lists of numbers generated by functions with natural numbers as inputs. It covers various types of sequences, including arithmetic and geome...This section introduces sequences, defining them as ordered lists of numbers generated by functions with natural numbers as inputs. It covers various types of sequences, including arithmetic and geometric, and explains how to represent sequences explicitly and recursively. The section also discusses limits of sequences and provides examples to illustrate how sequences behave, helping readers understand convergence and divergence.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_III%3A_Series_and_Vector_Calculus/01%3A_Sequences_and_Series/1.01%3A_SequencesIn this section, we introduce sequences and define what it means for a sequence to converge or diverge. We show how to find limits of sequences that converge, often by using the properties of limits f...In this section, we introduce sequences and define what it means for a sequence to converge or diverge. We show how to find limits of sequences that converge, often by using the properties of limits for functions discussed earlier. We close this section with the Monotone Convergence Theorem, a tool we can use to prove that certain types of sequences converge.
- https://math.libretexts.org/Courses/Las_Positas_College/Book%3A_College_Algebra/08%3A_Sequences_Probability_and_Counting_Theory/8.02%3A_Sequences_and_Their_NotationsOne way to describe an ordered list of numbers is as a sequence. A sequence is a function whose domain is a subset of the counting numbers. Listing all of the terms for a sequence can be cumbersome. F...One way to describe an ordered list of numbers is as a sequence. A sequence is a function whose domain is a subset of the counting numbers. Listing all of the terms for a sequence can be cumbersome. For example, finding the number of hits on the website at the end of the month would require listing out as many as 31 terms. A more efficient way to determine a specific term is by writing a formula to define the sequence.
- https://math.libretexts.org/Courses/Mission_College/Math_001%3A_College_Algebra_(Kravets)/09%3A_Sequences_and_Series/9.01%3A_Sequences_and_Their_NotationsOne way to describe an ordered list of numbers is as a sequence. A sequence is a function whose domain is a subset of the counting numbers. Listing all of the terms for a sequence can be cumbersome. F...One way to describe an ordered list of numbers is as a sequence. A sequence is a function whose domain is a subset of the counting numbers. Listing all of the terms for a sequence can be cumbersome. For example, finding the number of hits on the website at the end of the month would require listing out as many as 31 terms. A more efficient way to determine a specific term is by writing a formula to define the sequence.
- https://math.libretexts.org/Courses/Chabot_College/Chabot_College_College_Algebra_for_BSTEM/09%3A_Sequences_Probability_and_Counting_Theory/9.01%3A_Sequences_and_Their_NotationsOne way to describe an ordered list of numbers is as a sequence. A sequence is a function whose domain is a subset of the counting numbers. Listing all of the terms for a sequence can be cumbersome. F...One way to describe an ordered list of numbers is as a sequence. A sequence is a function whose domain is a subset of the counting numbers. Listing all of the terms for a sequence can be cumbersome. For example, finding the number of hits on the website at the end of the month would require listing out as many as 31 terms. A more efficient way to determine a specific term is by writing a formula to define the sequence.
- https://math.libretexts.org/Workbench/MAT_2420_Calculus_II/05%3A_Sequences_and_Series/5.02%3A_SequencesIn this section, we introduce sequences and define what it means for a sequence to converge or diverge. We show how to find limits of sequences that converge, often by using the properties of limits f...In this section, we introduce sequences and define what it means for a sequence to converge or diverge. We show how to find limits of sequences that converge, often by using the properties of limits for functions discussed earlier. We close this section with the Monotone Convergence Theorem, a tool we can use to prove that certain types of sequences converge.
