Sequences & Series
What is Sequences & Series?
A sequence is a set of numbers in a particular order. A series is the sum of the consecutive terms in a sequence. Sequences and series can be written in mathematical notation using summation symbols.
Some types of sequences are arithmetic, where each term is separated from the previous term by a constant difference. For example, the sequence 5, 10, 15, 20 is an arithmetic sequence with common difference 5. Geometric sequences have a common ratio between terms. For example, the sequence 2, 6, 18, 54 is a geometric sequence with common ratio 3.
Fibonacci numbers form a sequence where each term is the sum of the previous two terms. This sequence appears in nature in the spirals of shells and in the arrangement of leaves on a stem.
The study of sequences and series can help us to find patterns and to make predictions. It is also useful in solving mathematical problems.
Sequences & Series Resources
Life of Fred: Real Analysis
Real Analysis is a topic studied by math majors in college. This math is more advanced than what most non-majors ever see, but it still has Fred, and he has a very good time with his favorite topic. Real Analysis is the study of real numbers, functio...
Calculus Two: Sequences and Series
Calculus Two: Sequences and Series is an introduction to sequences, infinite series, convergence tests, and Taylor series. The course emphasizes not just getting answers, but asking the question “why is this true?”...
Sequence and Series Video Tutorial
Video tutorials on sequences and series. Lot of different tests and techniques are discussed!...
Sequences, series, and function approximation
Now we switch gears away from integration to talk about sequences and series. Much of calculus is about dealing with infinity, and this topic has us dancing very closely with infinity itself. Sequences are infinite lists, series are infinite sums, an...