Series

Definition

$\sum _{n=1}^{\infty }{a}_n$ where $a_n$ is a term of a Sequence $(a_n)$

The operation of adding the terms of Sequence one after another.

Partial sum

$S_n=\sum _{k=1}^n{a}_k$

The summation of the $n$ first terms of a Sequence

Rearranged Series

${\sum }_{n=1}^{\infty }{a}_{f(n)}$ where $f:\mathbb{N}\to \mathbb{N}$ is Bijective function.

A series that is obtained by changing the order of terms in an original series’ Sequence.