# Error in book ?

1. Mar 10, 2007

### malawi_glenn

Hi i found this "error" in my text book in series.

https://www.physicsforums.com/attachment.php?attachmentid=9420&stc=1&d=1173538014

This is a geometric one, it converges for |z|< 1/rot(2) when i calculate this, but the text book claims that |z|<1/2

I also checked different values on z and i get a finite value even when z is 0,7
[ 0,5< 0,7 < 1/rot(2) ]

Who is right?

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2. Mar 10, 2007

### andytoh

An error in a textbook? I've never seen such a thing before!!!

Why do you think a book is constantly revised with newer editions?

3. Mar 10, 2007

### matt grime

How did you evaluate an infinite sum in a finite time?

4. Mar 10, 2007

### AlephZero

If the result is true when $$|z| < 1/\sqrt 2$$, then it is true when $$|z| < 1/2$$.

So what's the error?

5. Mar 10, 2007

### malawi_glenn

Yes of course i know that books don't have right all the time, but scince i didn't find that in the errata, i wanted to ask others to see if i was right or not.. why are you all so upset?!? Why cant you just confirm my discovery so that i can report this to the author?

And yes, of course |z| < 1/2 is ONE solution, but the author is giving the COMPLETE solution in all other places in the book, so you must be consistent...

And its not that hard to check if an geometric series is convergent or divergent.. just take n=156 on your calculator than you take 157 etc, and you see if the value is getting close to 1/(1-x) ... (if x is the argument in your geometric series)... The value of a geometric serie is less than unity if the serie converges as n goes to infinity..

6. Mar 11, 2007

### matt grime

So you put a few terms into a calculator and decided that was the behaviour for infinitely many terms? That isn't how you prove things.

It does look like a mistake, by the way.

7. Mar 11, 2007

### malawi_glenn

I never stated that i PROOVED, i checked.. and as i said, for a geometric serie it is a trivial thing to see..

8. Mar 11, 2007

### Gib Z

Yea matt I do that sometimes as well, it doesn't prove anything at all, but sometimes its obvious what its converging to, can give you a tiny prod in the right direction.

9. Mar 11, 2007

### matt grime

If you check it, then you demonstrate it to be true, i.e. you prove it. Numerical things like this merely suggest, they do not verify.

10. Mar 11, 2007

### malawi_glenn

No i checked if the sum SEEMED to reach a finite value for different |z|, THATS WHY i asked if my assumptions were correct.

Why cant you just answer my questions in the first place? Why must everybody be so besserwisser? "omg an error in textbook, no way", those kind of things.. And "well if it is true for |z|<1/rot2 , than it is also true for |z|<1/2", are you all in a bad mood or so? Why can't you be helpful?!

11. Mar 11, 2007

### Gib Z

We're trying to be helpful, please note these are people who are not getting paid to answer your questions! These people are very knowledgeable people who could better use their time! If you think they are being pedantic, hack it, your getting free advice from smart people!

12. Mar 11, 2007

### malawi_glenn

Treat your neighbour as you self want to be treated..

13. Mar 11, 2007

### matt grime

you have been answered on this topic.

it's irony. mistakes in textbooks are very frequent, and almost not worth pointing out.

this was pointing out that it wasn't clear if you were asking for a sufficient condition or a necessary and sufficient condition.

If you had said that the book asserted the radius of convergence was something, then that would be different. What you wrote is, if as litereally appears in the book, perfectly correct. That sum does converge for |z|<1/2. That is not the radius of convergence, but that is strictly a different matter from what you asked.