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    the answer to part c is x<1/2

    But I have no idea how to work that out.
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    (Original post by suibster)
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    the answer to part c is x<1/2

    But I have no idea how to work that out.
    when you get the partial fractions, say if one of them is (1-2x)^-1 then you get 1 + (-1)(-2x) + (-1)(-2)(-2x)/2

    the 2x bit is the key

    |2x| <1

    so |x| <1/2
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    Thanks but I don't really understand the thought process into this.
    why (1-2x)^-1 in particular ?
    There's also a bracket for (1-x)^-1 and (1-x)^-2, do you not take them into consideration?
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    (Original post by suibster)
    Thanks but I don't really understand the thought process into this.
    why (1-2x)^-1 in particular ?
    There's also a bracket for (1-x)^-1 and (1-x)^-2, do you not take them into consideration?
    You do, so you need all of

    |-x| < 1 AND |-x| < 1 AND |2x| < 1.

    But this simplifies down to just

    |x| < 1/2.

    Since if that's true then all three are true that the same time.

    Your thought process should be to always take the smallest bound you can. So if there was a (1-3x)^n in there, you'd also do |3x| < 1.
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    (Original post by Zacken)
    You do, so you need all of

    |-x| < 1 AND |-x| < 1 AND |2x| < 1.

    But this simplifies down to just

    |x| < 1/2.

    Since if that's true then all three are true that the same time.

    Your thought process should be to always take the smallest bound you can. So if there was a (1-3x)^n in there, you'd also do |3x| < 1.

    Thank you! Very well explained.
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    (Original post by suibster)
    Thank you! Very well explained.
    No worries, thank you. Appreciated.
 
 
 
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