Search
- Filter Results
- Location
- Classification
- Include attachments
- https://math.libretexts.org/Courses/Saint_Mary's_College_Notre_Dame_IN/SMC%3A_MATH_339_-_Discrete_Mathematics_(Rohatgi)/Text/2%3A_Sequences/2.1%3A_DefinitionsWhile we often just think of sequences as an ordered list of numbers, they really are a type of function. Later we will manipulate sequences in much the same way you have manipulated functions in alge...While we often just think of sequences as an ordered list of numbers, they really are a type of function. Later we will manipulate sequences in much the same way you have manipulated functions in algebra or calculus. We can shift a sequence up or down, add two sequences, or ask for the rate of change of a sequence. These are done exactly as you would for functions.
- 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/Cosumnes_River_College/Math_370%3A_Precalculus/07%3A_Sequences_and_the_Binomial_Theorem/7.01%3A_SequencesIn this section, we introduce sequences which are an important class of functions whose domains are the set of natural numbers.
- 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/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/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/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/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_(Levin)/2%3A_Sequences/2.1%3A_DefinitionsWhile we often just think of sequences as an ordered list of numbers, they really are a type of function. Later we will manipulate sequences in much the same way you have manipulated functions in alge...While we often just think of sequences as an ordered list of numbers, they really are a type of function. Later we will manipulate sequences in much the same way you have manipulated functions in algebra or calculus. We can shift a sequence up or down, add two sequences, or ask for the rate of change of a sequence. These are done exactly as you would for functions.
- https://math.libretexts.org/Bookshelves/Precalculus/Corequisite_Companion_to_Precalculus_(Freidenreich)/8%3A_Problem_Solving/8.01%3A_Arithmetic_SequencesWe can describe a sequence in words (e.g. a sequence of even numbers.) but can we describe the sequence mathematically? That is, can we describe the pattern of the sequence of even numbers using a for...We can describe a sequence in words (e.g. a sequence of even numbers.) but can we describe the sequence mathematically? That is, can we describe the pattern of the sequence of even numbers using a formula? Absolutely! This section will explore arithmetic sequences, how to identify them, mathematically describe their terms, and the relationship between arithmetic sequences and linear functions. Let’s get started!
- 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.
