Turn on thread page Beta
    Offline

    8
    ReputationRep:
    I wanted to link to this thread earlier, but I didn't want to ruin the hint!
    Offline

    18
    ReputationRep:
    (Original post by Piecewise)
    I wanted to link to this thread earlier, but I didn't want to ruin the hint!
    Although it still doesn't show differentiating the sum does what you want, and to be honest I'm not convinced the OP has either. (Weierstrauss M-test shows the result of differentiating term by term converges uniformly, but that doesn't directly prove it converges to the result of differentiating the expression for the sum).

    Edit: (to be clear, what you've posted is fine for normal pre-uni maths, but it isn't a proof).
    Offline

    8
    ReputationRep:
    (Original post by DFranklin)
    Edit: (to be clear, what you've posted is fine for normal pre-uni maths, but it isn't a proof).
    Just to be safe, is it fine, say, for the STEP?
    Offline

    10
    ReputationRep:
    (Original post by DFranklin)
    Although it still doesn't show differentiating the sum does what you want, and to be honest I'm not convinced the OP has either. (Weierstrauss M-test shows the result of differentiating term by term converges uniformly, but that doesn't directly prove it converges to the result of differentiating the expression for the sum).
    It's halfway there though. I remember a first-year proof without uniform convergence. It was hard and ugly. Then in second year we got a much easier proof, admittedly assuming the fundamental theorem of calculus among other things.
    Offline

    18
    ReputationRep:
    (Original post by Piecewise)
    Just to be safe, is it fine, say, for the STEP?
    Yes.
    Offline

    18
    ReputationRep:
    (Original post by Zhen Lin)
    It's halfway there though. I remember a first-year proof without uniform convergence. It was hard and ugly.
    It's really not that hard to find the finite sum and then take the limit.

    Then in second year we got a much easier proof, admittedly assuming the fundamental theorem of calculus among other things.
    Sure. But as I said, it's not exactly a "obvious" consequence of uniform convergence.
    Offline

    10
    ReputationRep:
    (Original post by DFranklin)
    It's really not that hard to find the finite sum and then take the limit.
    Hmmm. It wasn't that easy, as I recall... Lemma 9.6 and theorem 9.7 here (p.40-41).
    Offline

    18
    ReputationRep:
    (Original post by Zhen Lin)
    Hmmm. It wasn't that easy, as I recall... Lemma 9.6 and theorem 9.7 here (p.40-41).
    Well, it's also not that hard (it's all really mechanical use of basic technique, although it is a little long).

    But I was actually meaning the specific question "find the sum of the first n terms of k/2^k", which is quite easy.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: March 28, 2011

University open days

  1. University of Cambridge
    Christ's College Undergraduate
    Wed, 26 Sep '18
  2. Norwich University of the Arts
    Undergraduate Open Days Undergraduate
    Fri, 28 Sep '18
  3. Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 29 Sep '18
Poll
Which accompaniment is best?
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

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.