# Series in Mathematics

This post talks about the concept “series” in mathematics, along with the definition , the Partial Sum and the notation of the series.Series in mathematics, is the widely used operation. It is based upon the term’Partial Sum’. Here is discussed the Definition along with the notation of the series.

Let us start from the Definition of the series, then we’ll go accordingly…

# Series- Definition:

Series is nothing but the infinite (or finite) sum of the elements in a sequence. We write it as follows:∞

**∑ _{n=1}^{∞} (X )= X_{1} + X_{2} + . . .**

Above is an infinite series. In order to define series, we first discuss the term “Partial Sum”.

## Partial Sum:

Suppose, we have a sequence of ‘n’ elements, then the sum of these ‘n’ elements, denote it as -<S_{n}>, will be the Partial sum of ‘n’ elements.

In essence, we are taking partial sum of ‘n’ numbers in the sequence<X_{n}>,

Partial Sum :<S_{n}> = X_{1} + X_{2} + . . . + X_{n}.

## Notation of Series:

Notation for the series is as follows :

∑_{n=1}^{∞} (X ) , ∑_{n=1}^{3} (a ) , ∑_{n=1}^{n} (S ) , etc…

Generally, series is just the sum, so, summation symbol denotes it.

There are various types of the Series in Mathematics, Here, we discuss some of them . . .

- Convergent Series
- Geometric Series
- Power Series
- Taylor’s Series
- Maclaurin’s Series

are some of them.. That we’ll discuss accordingly. Also, there are some tests for checking the convergence of the Series, which we’ll cover in the next posts…