You are Here: Home >< Maths

# Simple Question: Is this correct? watch

Announcements
1. Hey.

Something I am reading through states:

"If you have written the series for log(1 + x) as 1-x+(x^2)/2-(x^3)/3+...
then a quick check will reveal that it doesn’t work for x = 0; clearly, the 1 should not be there.

"Another check will reveal that for very small positive x, log is positive (since its argument is bigger than 1) whereas the series is negative, so there is clearly something else wrong."

Is the second paragraph correct? If x is small and positive, I interpret that as meaning 0<x<1 in this case. Hence, subsequent terms of the series will become smaller in magnitude and, due to the fact that the sign of each term alternates between being positive and negative, the sequence will continue to oscillate with ever-decreasing amplitude and the sum will converge to a number y, where (1-x)<y<1.

If this is all true, then why does it state the series is negative?
2. yes it is wrong. but that isn't even the expansion for log so I'm confused as to why they're even discussing it.
3. (Original post by Chewwy)
yes it is wrong. but that isn't even the expansion for log so I'm confused as to why they're even discussing it.

Page 8 of this booklet. Right at the very bottom of the page. The professor is discussing what you can do if you have got going with a problem but then appear to have hit some invisible barrier. He suggests checking your workings etc. and looking for mistakes which is what this is relating to. However, it surprises me that he would have written something incorrectly seeing as he is a don at Mathematics. Hence, the reason why I have made this thread.
4. What he means is even after you remove the 1 that shouldn't be there, you can tell there's another problem because the sign is wrong for x small and positive. (But you need to remove the 1 first).
5. (Original post by DFranklin)
What he means is even after you remove the 1 that shouldn't be there, you can tell there's another problem because the sign is wrong for x small and positive. (But you need to remove the 1 first).
Thank-you. I thought I must have been missing something because he would not make such a mistake!

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: March 13, 2011
Today on TSR

### Moving into halls?

How do unis decide who goes where?

### University open days

• University of Lincoln
Wed, 12 Dec '18
• Bournemouth University
Midwifery Open Day at Portsmouth Campus Undergraduate
Wed, 12 Dec '18
• Buckinghamshire New University
Wed, 12 Dec '18
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