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# C4 really hard question need help :)

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1. the answer to part c is x<1/2

But I have no idea how to work that out.
2. (Original post by suibster)

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
3. 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?
4. (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.
5. (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.
6. (Original post by suibster)
Thank you! Very well explained.
No worries, thank you. Appreciated.

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