Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    6
    ReputationRep:
    https://www.youtube.com/watch?time_c...&v=twH9iZbXyKU

    When proving this, why did he use the equation he's trying to prove for the Kth term and the other equation for (K+1)? thanks
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    (Original post by Maths&physics)
    https://www.youtube.com/watch?time_c...&v=twH9iZbXyKU

    Its ok, I got help with that last question, thanks. When proving this, why did he use the equation he's trying ti prove for the Kth term and the other equation for (K+1)? thanks

    Because that's how induction works.

    He assumed that the proposition, which is u_n=2n^2-4n+6-2^{-n}, to be TRUE for n=k.

    This clearly means that we now have u_k=2k^2-4k+6-2^{-k} as a TRUE relation that we can use.


    When you move onto n=k+1, you need to start with recurrence relation, so when writing down u_{k+1} you need to use the recurrence relation. The key part is then using the inductive assumption and put it INSIDE the first relation, and simplify to show the second relation is true for n=k+1. So you need to work with both - it's a basic principle of induction.
    • Thread Starter
    Offline

    6
    ReputationRep:
    (Original post by RDKGames)
    Because that's how induction works.

    He assumed that the proposition, which is u_n=2n^2-4n+6-2^{-n}, to be TRUE for n=k.

    This clearly means that we now have u_k=2k^2-4k+6-2^{-k} as a TRUE relation that we can use.


    When you move onto n=k+1, you need to start with recurrence relation, so when writing down u_{k+1} you need to use the recurrence relation. The key part is then using the inductive assumption and put it INSIDE the first relation, and simplify to show the second relation is true for n=k+1. So you need to work with both - it's a basic principle of induction.
    thanks
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    Notnek bit of a disaster with the moving of posts here, now I'm the thread starter since I posted the response before he made this thread. Fix pls

    (Original post by Maths&physics)
    thanks
    Best if you just create new threads with appropriate titles corresponding to your topic question whenever you need to ask something.
    • Thread Starter
    Offline

    6
    ReputationRep:
    (Original post by RDKGames)
    Notnek bit of a disaster with the moving of posts here, now I'm the thread starter since I posted the response before he made this thread. Fix pls



    Best if you just create new threads with appropriate titles corresponding to your topic question whenever you need to ask something.
    I will do. thanks again
    • TSR Support Team
    • Study Helper
    Offline

    20
    ReputationRep:
    (Original post by RDKGames)
    Notnek bit of a disaster with the moving of posts here, now I'm the thread starter since I posted the response before he made this thread. Fix pls
    I just changed the time of your post and that's fixed it.
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    (Original post by Notnek)
    I just changed the time of your post and that's fixed it.
    Didn't even know that was a thing mods can do lol
    • Thread Starter
    Offline

    6
    ReputationRep:
    (Original post by RDKGames)
    Didn't even know that was a thing mods can do lol
    its ok. I got it.
    • TSR Support Team
    • Study Helper
    Offline

    20
    ReputationRep:
    (Original post by RDKGames)
    Didn't even know that was a thing mods can do lol
    It's not something we're meant to do regularly. But it can be tempting to bump threads by changing the post time
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Did TEF Bronze Award affect your UCAS choices?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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