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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 560

I have to find the series for g(x) = -ln(1-x) using the function f(x) = 1/(1-x).

Seems simple as f(x) is just the derivative of g(x).

So I start by finding the series for 1/(1-x) =

k=0 to inf.Now I am dont know where to go from here, I can integrate the whole series but that doesnt get me the right answer.

I also tried to work the series from ln(x) to -ln(1-x) but also got stuck.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,048

What do you get when you integrate the series for 1/(1-x) ?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,278

hi careless25,

Your integration method does work and your series for 1/(1-x) is correct.

So I have the same question as anonimnystefy, what did you get and why did you think it was wrong?

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi careless25;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 560

Yea I get your answer bobbym but wolfram gives another representation.

http://www.wolframalpha.com/input/?i=-l … esentation

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,278

If you mean this (see picture below), then it is the same. There are 2k minus signs there and that will work out to be +

That's the problem with getting a computer to work it out ... you may not get the simplest form.

It happened to me recently with an integration involving trig. Took 3 lines of working to change Wolfram's version into mine.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 560

Thanks! That explains a lot.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,048

As Bob said,you will not always get the simplest form from a computer, but, speaking in bobbym's name, more often you will. So don't discard computers right away.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

Yea I get your answer bobbym but wolfram gives another representation.

Alpha's representation are often a little different. It does not reason the same way as we do. Different methods can sometimes produce the same answer in different forms.

But the series for 1 / ( 1 - x ) is a well know one in combinatorics so you will not need a computer. You can just integrate the general term.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,048

Ah,the most beautiful generating function.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

One last beef:

Although I applaud Wolfram for doing something for everyone to benefit by I have repeatedly emailed them about getting Alpha to understand Mathematica's syntax!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,048

You mean,so that you can use either?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Yes, Wolfram is a bit like a guy I knew who would use an English to English book to watch Benny Hill!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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