You are Here: Home >< Maths

# Converging series Watch

1. Firstly what does converge mean exactly; I think I know what it means but I'm not 100% sure. I believe it means when the a series goes towards a number.
Any ways I don't understand how when -1 < x < 3 it converges. When x = 2 I think it goes to infinity as all the terms are being added up ( you get 1 + 0.5 + 0.25 +... numbers get smaller).
2. As the number of terms tends to infinite, the summation will tend towards one value if the series converges.

I'm afraid I can't help with the actual question - I don't know that much about sequences and series.
3. (Original post by WinOrDie)

Firstly what does converge mean exactly; I think I know what it means but I'm not 100% sure. I believe it means when the a series goes towards a number.
Any ways I don't understand how when -1 < x < 3 it converges. When x = 2 I think it goes to infinity as all the terms are being added up ( you get 1 + 0.5 + 0.25 +... numbers get smaller).
Convergence means existing finite limit.

For function series this means a limit function.
For

the radius of convergence around c is

So

So the series convergent around 1 with radius of 2, that is
4. (Original post by ztibor)
Convergence means existing finite limit.

For function series this means a limit function.
For

the radius of convergence around c is

So

So the series convergent around 1 with radius of 2, that is
what does [Sum off] An.Fn(x-c) mean?
5. (Original post by WinOrDie)
what does [Sum off] An.Fn(x-c) mean?
a function series is a series, where the summands are not just real or complex numbers but functions.
Examples of function series include power series, Laurent series, Fourier series, etc.

For power series
http://en.wikipedia.org/wiki/Power_series
6. (Original post by WinOrDie)

Firstly what does converge mean exactly; I think I know what it means but I'm not 100% sure. I believe it means when the a series goes towards a number.
Any ways I don't understand how when -1 < x < 3 it converges. When x = 2 I think it goes to infinity as all the terms are being added up ( you get 1 + 0.5 + 0.25 +... numbers get smaller).
Are you studying this as part of a course or have you just found this question at random?

You're asking about series convergence but you don't seem terribly clear on what the question's asking, so I'm not sure what level you're working at

Does "geometric series" ring any bells?

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 18, 2014
Today on TSR

### 8 things that will happen during Freshers

Don't say we didn't warn you...

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams