Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    I'm wondering if someone could help me with part (c), I'm not sure how to start it at all. Also I would be thankful if someone could also quickly verify my solutions to (a) and (b), especially (a) as I just assumed the ds changes to dx at the end but I don't know if this is correct..?
    Attached Images
      
    • Thread Starter
    Offline

    0
    ReputationRep:
    Anyone?
    Offline

    18
    ReputationRep:
    (Original post by BahamutXV)
    Anyone?
    The given result doesn't seem to be true.

    Take N=1, v0 = 1, v1=0. Then the 2nd sum in the rhs product is zero, the LHS isn't.

    This isn't just nitpicking; I think it's clear the difficulty in proving this is what happens at 0 and N in the RHS sums.
    Offline

    12
    ReputationRep:
    (Original post by DFranklin)
    The given result doesn't seem to be true.

    Take N=1, v0 = 1, v1=0. Then the 2nd sum in the rhs product is zero, the LHS isn't.

    This isn't just nitpicking; I think it's clear the difficulty in proving this is what happens at 0 and N in the RHS sums.
    You're meant to assume v_0 = 0.

    Anyway, bound the |v_k + v_{k-1}| term by |v_k| + |v_{k-1}|. This is where the two will come from.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by IrrationalNumber)
    You're meant to assume v_0 = 0.

    Anyway, bound the |v_k + v_{k-1}| term by |v_k| + |v_{k-1}|. This is where the two will come from.
    This is what I ended up getting but I'm still not sure where the 2 comes from? I assumed the 2 would just be in the continuous case as in part (a), not the discrete.

    Name:  cauchy3c1.jpg
Views: 34
Size:  64.3 KB
    Offline

    18
    ReputationRep:
    (Original post by IrrationalNumber)
    You're meant to assume v_0 = 0.

    Anyway, bound the |v_k + v_{k-1}| term by |v_k| + |v_{k-1}|. This is where the two will come from.
    Oops, thanks!

    (Original post by BahamutXV)
    This is what I ended up getting but I'm still not sure where the 2 comes from? I assumed the 2 would just be in the continuous case as in part (a), not the discrete.
    If you write out the sum \sum_{k=1}^N |v_k| + |v_{k-1}| for small N, you'll see you end up with a lot of repeated terms. This is where the 2 is going to come from. There's still a little fiddling you'll need to do to deal with the end conditions.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by DFranklin)
    Oops, thanks!

    If you write out the sum \sum_{k=1}^N |v_k| + |v_{k-1}| for small N, you'll see you end up with a lot of repeated terms. This is where the 2 is going to come from. There's still a little fiddling you'll need to do to deal with the end conditions.
    Thank you for your help!
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 8, 2017

University open days

  • University of Roehampton
    All departments Undergraduate
    Sat, 17 Nov '18
  • Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 17 Nov '18
  • Bournemouth University
    Undergraduate Open Day Undergraduate
    Sat, 17 Nov '18
Poll
Black Friday: Yay or Nay?
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.