Turn on thread page Beta

Simple Question: Is this correct? watch

Announcements
    • Thread Starter
    Offline

    3
    ReputationRep:
    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?
    Offline

    15
    ReputationRep:
    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.
    • Thread Starter
    Offline

    3
    ReputationRep:
    (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.
    http://www.admissionstests.cambridge...s_-_Master.pdf

    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.
    Offline

    18
    ReputationRep:
    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).
    • Thread Starter
    Offline

    3
    ReputationRep:
    (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!
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: March 13, 2011

University open days

  • University of Lincoln
    Brayford Campus Undergraduate
    Wed, 12 Dec '18
  • Bournemouth University
    Midwifery Open Day at Portsmouth Campus Undergraduate
    Wed, 12 Dec '18
  • Buckinghamshire New University
    All undergraduate Undergraduate
    Wed, 12 Dec '18
Poll
Do you like exams?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.