Series Is Math

Definition of a series.

Series is math. For instance a 8 2 8 3 16 3 19 in words a n 2n 3 can be read as the n th term is given by two enn plus three. This list of mathematical series contains formulae for finite and infinite sums. Provides worked examples of typical introductory exercises involving sequences and series. Demonstrates how to find the value of a term from a rule how to expand a series how to convert a series to sigma notation and how to evaluate a recursive sequence.

The study of series is a major part of calculus and its generalization mathematical analysis series are used in most areas of mathematics even for studying finite structures such as in combinatorics through generating functions. The p series diverges if the common exponent is less than or equal to 1 which is in sharp comparison with the harmonic series. Is the riemann zeta function is the gamma function is a polygamma function is a polylogarithm. We will also give many of the basic facts properties and ways we can use to manipulate a series.

A mathematical series is the sum of a list of numbers that are generating according to some pattern or rule. The values of a sequence the sum of which form a series are referred to as terms or elements. The series converges if the common ratio is clearly greater than 1. Since this series is made from a finite sequence and therefore contains a finite number of terms it s what s called a finite series.

Shows how factorials and powers of 1 can come into play. For example 1 3 5 7 9 is a mathematical series the sum of. For instance if the formula for the terms a n of a sequence is defined as a n 2n 3 then you can find the value of any term by plugging the value of n into the formula. We will then define just what an infinite series is and discuss many of the basic concepts involved with series.

Though the value of the sum at this point is only known in a few instances. Sequences and series are most useful when there is a formula for their terms. And as a. Here is taken to have the value is a bernoulli polynomial is a bernoulli number and here.

We will also briefly discuss how to determine if an infinite series will converge or diverge a more in depth discussion of this topic will occur in the next section. Series are largely used in calculus as well as in other areas of mathematics physics computer science statistics and finance. We discuss whether a sequence converges or diverges is increasing or decreasing or if the sequence is bounded. In mathematics a series can be generally described as the sum of an infinite sequence of values.

In this chapter we introduce sequences and series. On the other hand since the fibonacci sequence is an infinitely long sequence of numbers the series formed by adding together all the fibonacci numbers is what s called an infinite series. Is an euler number. In this section we will formally define an infinite series.