Definition (Sequence of Real Numbers) A sequence of real numbers is a function Z∩(n,∞) → R for some real number n. Don’t let the description of the domain confuse you; it’s just a fancy way of saying the domain consists of a set of consecutive integers starting with some integer but never ending. In most cases, the domain will be either the set of positive integers or the set of non-negative integers. Try to recognize that the entire definition is just a fancy, but precise, way of saying a sequence is a list of numbers. We can have sequences of objects other than real numbers, but in this course we will restrict ourselves to sequences of real numbers and will from now on just refer to sequences. Sequences A sequence is essentially just a list. AlanH.SteinUniversityofConnecticut SequencesandSeries Don’t let the description of the domain confuse you; it’s just a fancy way of saying the domain consists of a set of consecutive integers starting with some integer but never ending. In most cases, the domain will be either the set of positive integers or the set of non-negative integers. Try to recognize that the entire definition is just a fancy, but precise, way of saying a sequence is a list of numbers. We can have sequences of objects other than real numbers, but in this course we will restrict ourselves to sequences of real numbers and will from now on just refer to sequences. Sequences A sequence is essentially just a list. Definition (Sequence of Real Numbers) A sequence of real numbers is a function Z∩(n,∞) → R for some real number n. AlanH.SteinUniversityofConnecticut SequencesandSeries In most cases, the domain will be either the set of positive integers or the set of non-negative integers. Try to recognize that the entire definition is just a fancy, but precise, way of saying a sequence is a list of numbers. We can have sequences of objects other than real numbers, but in this course we will restrict ourselves to sequences of real numbers and will from now on just refer to sequences. Sequences A sequence is essentially just a list. Definition (Sequence of Real Numbers) A sequence of real numbers is a function Z∩(n,∞) → R for some real number n. Don’t let the description of the domain confuse you; it’s just a fancy way of saying the domain consists of a set of consecutive integers starting with some integer but never ending. AlanH.SteinUniversityofConnecticut SequencesandSeries Try to recognize that the entire definition is just a fancy, but precise, way of saying a sequence is a list of numbers. We can have sequences of objects other than real numbers, but in this course we will restrict ourselves to sequences of real numbers and will from now on just refer to sequences. Sequences A sequence is essentially just a list. Definition (Sequence of Real Numbers) A sequence of real numbers is a function Z∩(n,∞) → R for some real number n. Don’t let the description of the domain confuse you; it’s just a fancy way of saying the domain consists of a set of consecutive integers starting with some integer but never ending. In most cases, the domain will be either the set of positive integers or the set of non-negative integers. AlanH.SteinUniversityofConnecticut SequencesandSeries We can have sequences of objects other than real numbers, but in this course we will restrict ourselves to sequences of real numbers and will from now on just refer to sequences. Sequences A sequence is essentially just a list. Definition (Sequence of Real Numbers) A sequence of real numbers is a function Z∩(n,∞) → R for some real number n. Don’t let the description of the domain confuse you; it’s just a fancy way of saying the domain consists of a set of consecutive integers starting with some integer but never ending. In most cases, the domain will be either the set of positive integers or the set of non-negative integers. Try to recognize that the entire definition is just a fancy, but precise, way of saying a sequence is a list of numbers. AlanH.SteinUniversityofConnecticut SequencesandSeries Sequences A sequence is essentially just a list. Definition (Sequence of Real Numbers) A sequence of real numbers is a function Z∩(n,∞) → R for some real number n. Don’t let the description of the domain confuse you; it’s just a fancy way of saying the domain consists of a set of consecutive integers starting with some integer but never ending. In most cases, the domain will be either the set of positive integers or the set of non-negative integers. Try to recognize that the entire definition is just a fancy, but precise, way of saying a sequence is a list of numbers. We can have sequences of objects other than real numbers, but in this course we will restrict ourselves to sequences of real numbers and will from now on just refer to sequences. AlanH.SteinUniversityofConnecticut SequencesandSeries n is the independent variable, but when studying sequences we refer to it as the index. We’ll often define a sequence by giving a formula for a , just as we n often define an ordinary function f(x) by giving a formula. 1 Example: a = . This sequence can also be described by n n 1 1 1 1, , , ,.... 2 3 4 Example: b = n2. This sequence can also be described by n 1,4,9,16,25,... . Notation We generally use the notation {a } to denote a sequence, just as n we often use the notation f(x) to denote a function. AlanH.SteinUniversityofConnecticut SequencesandSeries We’ll often define a sequence by giving a formula for a , just as we n often define an ordinary function f(x) by giving a formula. 1 Example: a = . This sequence can also be described by n n 1 1 1 1, , , ,.... 2 3 4 Example: b = n2. This sequence can also be described by n 1,4,9,16,25,... . Notation We generally use the notation {a } to denote a sequence, just as n we often use the notation f(x) to denote a function. n is the independent variable, but when studying sequences we refer to it as the index. AlanH.SteinUniversityofConnecticut SequencesandSeries 1 Example: a = . This sequence can also be described by n n 1 1 1 1, , , ,.... 2 3 4 Example: b = n2. This sequence can also be described by n 1,4,9,16,25,... . Notation We generally use the notation {a } to denote a sequence, just as n we often use the notation f(x) to denote a function. n is the independent variable, but when studying sequences we refer to it as the index. We’ll often define a sequence by giving a formula for a , just as we n often define an ordinary function f(x) by giving a formula. AlanH.SteinUniversityofConnecticut SequencesandSeries Example: b = n2. This sequence can also be described by n 1,4,9,16,25,... . Notation We generally use the notation {a } to denote a sequence, just as n we often use the notation f(x) to denote a function. n is the independent variable, but when studying sequences we refer to it as the index. We’ll often define a sequence by giving a formula for a , just as we n often define an ordinary function f(x) by giving a formula. 1 Example: a = . This sequence can also be described by n n 1 1 1 1, , , ,.... 2 3 4 AlanH.SteinUniversityofConnecticut SequencesandSeries