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Math Help - Mathematical Induction and Recurrence

  1. #1
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    Mathematical Induction and Recurrence

    Hi,

    First of all, hi. Secondly if this is in the wrong place, sorry.

    I'm currently studying at Uni and our topic has now been started on. I haven't done any serious maths for a long, long time and I am struggling quite badly to understand what I am trying to do. I've read and re-read all my material but nothing is click, at the moment it is like another language to me and since this is the last part of my assignments this year I don't want to bring to down my average too much. So I was wondering if you could help me figure out this problem.


    U(0) = 8
    U(i)=17+2 U(i− 1) (i>0)

    Question:

    For an integer i,with i≥ 0, U(i) is defined by the recurrence system in part (a)(iii) see above, and F(i) is defined by the formula F(i)= 25 2i − 17. Prove by mathematical induction that U(i)= F(i) (for all integers iwith i≥ 0).

    I'll be honest, I have no idea where to start.

    Any help would be grateful.

    Thanks,
    John.
    Last edited by JohnD; May 20th 2009 at 05:21 AM.
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  2. #2
    MHF Contributor

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    Quote Originally Posted by JohnD View Post
    Hi,

    First of all, hi. Secondly if this is in the wrong place, sorry.

    I'm currently studying at Uni and our topic has now been started on. I haven't done any serious maths for a long, long time and I am struggling quite badly to understand what I am trying to do. I've read and re-read all my material but nothing is click, at the moment it is like another language to me and since this is the last part of my assignments this year I don't want to bring to down my average too much. So I was wondering if you could help me figure out this problem.


    U(0) = 8
    U(i)=17+2 U(i− 1) (i>0)

    Question:

    For an integer i,with i≥ 0, U(i) is defined by the recurrence system in part (a)(iii) see above, and F(i) is defined by the formula F(i)= 25 2i − 17. Prove by mathematical induction that U(i)= F(i) (for all integers iwith i≥ 0).

    I'll be honest, I have no idea where to start.

    Any help would be grateful.

    Thanks,
    John.
    I suspect that it actually says F(i)= 25(2^i)- 17, not F(i)= 25(2i)- 17. Well, you must show that it satisfies the equations given.

    It is easy to show that [quote]F(0)= 25(2^0)- 17= 25- 17= 8[/tex].

    Now you need to show that F(i)= 17+ 2F(i-1). F(i) is given above. F(i-1)= 25(2^{i-1})- 17. Put those into the formula and show that it is true.
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