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Math Help - Finding a recurrence relation

  1. #1
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    Question Finding a recurrence relation

    Can anyone help me solve part b for the following problem:

    a) Find the recurrence relation satisfied by an, where an is the number of regions that a plane is divided into by n lines, if no two of the lines are parallel and no three of the lines go through the same point.

    b) For the situation in part (a), let bn be the number of infinite regions that result. Find the recurrence relation for bn.

    I found my recurrence relation for part a, but is bn the sum of all regions found in a) or what?

    Thanks for any type of help you may provide me!
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  2. #2
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    Quote Originally Posted by precious_pearl13 View Post
    a) Find the recurrence relation satisfied by an, where an is the number of regions that a plane is divided into by n lines, if no two of the lines are parallel and no three of the lines go through the same point.

    b) For the situation in part (a), let bn be the number of infinite regions that result. Find the recurrence relation for bn.

    I found my recurrence relation for part a, but is bn the sum of all regions found in a) or what?
    every new line adds only two new infinite regions. thus: b_{n+1}=b_n + 2, \ \ n \geq 1, and b_1=2. therefore: b_n=2n, \ \ n \geq 1.
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  3. #3
    Bar0n janvdl's Avatar
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    In future, it is not necessary to tell us to delete your posts when you understand.
    Rather post a message thanking the user who helped you.

    (I think when you reach 10 posts you should be able to delete your own posts anyway.)
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