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Thread: Induction Help

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    Induction Help

    So I came across this induction question and am quite stuck mid-way.
    The question is: Prove that is divisible by for all odd integers

    So far, I have this working out done:

    1. To prove: , where
    Prove true for

    which is divisible by 3
    So the statement is true for

    2. Assume true for , where
    i.e. , where

    3. Prove true for
    To prove: , where


    Aaaand I'm stuck at that step. I've no idea how to manipulate the LHS so that the assumption from 2 can be subbed into 3. Also, is the working so far correct? Thanks!

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    Re: Induction Help

    Quote Originally Posted by alussovsky View Post
    So I came across this induction question and am quite stuck mid-way.
    The question is: Prove that is divisible by for all odd integers

    So far, I have this working out done:

    1. To prove: , where
    Prove true for

    which is divisible by 3
    So the statement is true for

    2. Assume true for , where
    i.e. , where

    3. Prove true for
    To prove: , where


    Aaaand I'm stuck at that step. I've no idea how to manipulate the LHS so that the assumption from 2 can be subbed into 3. Also, is the working so far correct? Thanks!

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    Re: Induction Help

    Also, thanks for posting your attempts!

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    Re: Induction Help

    Quote Originally Posted by alussovsky View Post
    So I came across this induction question and am quite stuck mid-way.
    The question is: Prove that is divisible by for all odd integers

    So far, I have this working out done:

    1. To prove: , where
    Prove true for

    which is divisible by 3
    So the statement is true for

    2. Assume true for , where
    i.e. , where

    3. Prove true for
    To prove: , where


    Aaaand I'm stuck at that step. I've no idea how to manipulate the LHS so that the assumption from 2 can be subbed into 3. Also, is the working so far correct? Thanks!
    some critisicm: when you say always say or since by only you can include the negative set which is Wrong. Since Induction USUALLY deals with


    Anyway, for step 2, the assumption satge I would say and for the proving step, I would let ; it makes it easier this way!

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    Re: Induction Help

    Quote Originally Posted by InteGrand View Post
    Thank you for the help! ... but I'm still a bit stuck on step 3, sorry ^^" How would you manipulate so that you can substitute the from the step 2 assumption?

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    Re: Induction Help

    Thank you for pointing that out! Even in written down working out, I keep forgetting that plus sign, so I'll make sure to check that it's in next time, haha.

    In class, my teacher said that when proving for odd integers, you should always use the assumption so that the odd integer 1 is not excluded! Is that true or is still alright to use ?

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    Re: Induction Help

    Quote Originally Posted by alussovsky View Post
    Thank you for the help! ... but I'm still a bit stuck on step 3, sorry ^^" How would you manipulate so that you can substitute the from the step 2 assumption?

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    Re: Induction Help

    Quote Originally Posted by InteGrand View Post
    I... think I get it?! Maybe?! Just to check,






    from previous assumption

    as since then

    ... which I hope is correct. Thank you for all of your help though!

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    Re: Induction Help

    Quote Originally Posted by alussovsky View Post
    I... think I get it?! Maybe?! Just to check,






    from previous assumption

    as since then

    ... which I hope is correct. Thank you for all of your help though!
    Well done! And no worries.

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    Re: Induction Help

    Quote Originally Posted by InteGrand View Post
    Well done! And no worries.
    Once again (you're probably sick of hearing this by this point XD) thank you so much for all your help!

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    Re: Induction Help

    Quote Originally Posted by alussovsky View Post
    Thank you for pointing that out! Even in written down working out, I keep forgetting that plus sign, so I'll make sure to check that it's in next time, haha.

    In class, my teacher said that when proving for odd integers, you should always use the assumption so that the odd integer 1 is not excluded! Is that true or is still alright to use ?

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