(adsbygoogle = window.adsbygoogle || []).push({}); infinite series!!

1. The problem statement, all variables and given/known data

Hi!!

I've learned that the definition of a sequence of elements of complex numbers is as follows;

a sequence is a function whose domain is a set of all positive integers with values in a set consisting of all complex numbers. (Denote the set of all complex numbers by C from now on)

Now, let {a[itex]_{n}[/itex]} be a sequence of elements of C.

Then, as you know, infinite series is defined as a sequence of partial sums b[itex]_{k}[/itex] = [itex]\sum[/itex][itex]^{k}_{n=1}[/itex]a[itex]_{n}[/itex].If the limit of the sequence exists, then it is said that the infinite series{b[itex]_{k}[/itex]} is convergent. In this case,

a value of the limit of the sequence is called a sum of the series and is denoted by

lim[itex]_{k\rightarrow}[/itex][itex]\infty[/itex]b[itex]_{k}[/itex].

Now, here is my question.

I've seen a notation like this; [itex]\sum[/itex][itex]_{n=p}[/itex][itex]^{\infty}[/itex]a[itex]_{n}[/itex] where p is any integer. If p is not 1, then I have no idea how to interpret this expression.....

What is the exact definition of a kind of a sum above..?

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Infinite series

**Physics Forums | Science Articles, Homework Help, Discussion**