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    Im currently revising FP2 and am doing Maclaurin series. I was wondering how you work out the validity for a series from its maclaurin series, and whether there was a general rule for how to work it out.

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    (Original post by Eux)
    Im currently revising FP2 and am doing Maclaurin series. I was wondering how you work out the validity for a series from its maclaurin series, and whether there was a general rule for how to work it out.

    Thankyou
    Radius of convergence. It's Uni material though, so don't expect to understand all of it.
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    (Original post by Zacken)
    Radius of convergence. It's Uni material though, so don't expect to understand all of it.
    So does that not mean we have to work out the validity for, say, arctan(0.5x-2)      OR ln(3x+5)
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    (Original post by Eux)
    So does that not mean we have to work out the validity for, say, arctan(0.5x-2)      OR ln(3x+5)
    Those are standard expansions, though. You should be able to derive them from the formula booklet immediately, give me a sec.
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    (Original post by Eux)
    So does that not mean we have to work out the validity for, say, arctan(0.5x-2)      OR ln(3x+5)
    You know \ln(1 +x) is valid for |x| \leq 1 so x \mapsto f(x) means the validity is restricted to |f(x)| \leq 1.

    Write \ln(3x+5) = \ln 5 + \ln \left(1 + \frac{3x}{5}\right) then the validity is \left|\frac{3x}{5}\right| \leq 1 \iff |x|\leq \frac{5}{3} which is your radius of convergence.

    P.S: I was doing my standard rounds on math.stack a few minutes earlier.
 
 
 
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