Power series (expansion series)

1. Mar 29, 2014

delsoo

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

hi, for the expansion of power series (logarithmitic series) , ln(1+X) , why the condition for x is between -1 and 1 which x can be 1 but x cant be -1 ?

2. Relevant equations

3. The attempt at a solution

2. Mar 29, 2014

Simon Bridge

3. Mar 29, 2014

delsoo

IF x--1 , then y=ln(0) , which is undefined , if |x|>1, i would get x less than- 1 and x more than 1 ... sub x value (less than -1 ), i would get ln(-x) which is also undefined, sub x value(more than 1 ), i would get ln (infinity) what does it represent?

Last edited: Mar 29, 2014
4. Mar 29, 2014

Simon Bridge

The power series you refer to is supposed to represent ln(x+1) ... so you have noticed that ln(x+1) is only defined for x>-1. This should tell you part of the answer to your question.

To understand the rest of your question, you have to refer to the series itself - what is the series?
What happens to the series when x=-1? Is this consistent with what happens to ln(x+1)?
What happens to the series when |x|>1? Is that consistent?

What I'm getting at is that the series is only valid for a narrow range of possible x values because those are the only values where the series, summed to infinity, is equal to ln(x+1).

5. Mar 29, 2014

delsoo

referring to my textbook, if x=1 , ln(1+X) converges, can you show me how it can converges please?

6. Mar 29, 2014

Simon Bridge

I can but I won't - that is perilously close to doing work for you, that you are best advised to do yourself.

You should be able to show yourself that it converges: consider what it means for a function to converge.
i.e. where does the power series coincide with the function?

You've run into this problem in other threads too.

Last edited: Mar 29, 2014