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Math Help - Linear Reccurence Sequence.

  1. #1
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    Linear Reccurence Sequence.

    How do you get from here.


    http://quicklatex.com/cache3/ql_6f21...760b746_l3.png


    to here?


    http://quicklatex.com/cache3/ql_5970...25731d8_l3.png

    Sorry about the links but site won't seem to accept the images as valid.

    Thanks.
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  2. #2
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    un-check the save to server when you insert the image in your post.
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  3. #3
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    Lexington, MA (USA)
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    Hello, AlyoshaKaz!

    How do you get from here.

    . . . . . . . . . . . . . . . . .r^{n-1} - 1
    X(n) . = . ar^{n-1} + --------------- d
    . . . . . . . . . . . . . . . . .. . r - 1

    to here?
    . . . . . . . . . . . . d . . . . . . . . . . . d
    X(n) . = . (a + -----) r^{n-1} .- .------
    . . . . . . . . . . .r - 1 . . . . . . . . . r - 1


    Get a common denomiantor and add:

    a(r - 1)r^{n-1} + (r^{n-1} - 1)d
    ---------------------------------------
    . . . . . . . . . . r - 1

    . . . . . a(r - 1)r^{n-1} + dr^{n-1} - d
    . . = . --------------------------------------
    . . . . . . . . . . . . . . . r - 1

    . . . . .a(r - 1)r^{n-1} . . dr^{n-1} . . d
    . . = . ------------------ + ----------- - ------
    . . . . . . . . r - 1 . . . . . . . .r - 1 . . . r - 1


    . . . . . . . . . . . . . dr^{n-1} . . d
    . . = . ar^{n-1} + ----------- - -----
    . . . . . . . . . . . . . . .r - 1 . . . r - 1

    . . . . . . . . . d . . . . . . . . . .d
    . . = . (a + -----)r^{n-1} - ------
    . . . . . . . . r - 1 . . . . . . . .r - 1


    I hope you could follow my steps . . .

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