Can somone please explain what they are asking? (Maclaurin Series)

**CainAndrews** · March 24th 2012, 05:25 PM

Hey everyone!

I'm trying to work on this assignment right now and I'm stuck on this question. I'm not to sure on what it wants. Here it is:

Starting from the Maclaurin series for 1/(1-x), find the Maclaurin series of ln(1+x^4)

If someone could start me off, that'd be awesome. Thanks!

**skeeter** · March 24th 2012, 05:57 PM

Originally Posted by CainAndrews

Hey everyone!

I'm trying to work on this assignment right now and I'm stuck on this question. I'm not to sure on what it wants. Here it is:

Starting from the Maclaurin series for 1/(1-x), find the Maclaurin series of ln(1+x^4)

If someone could start me off, that'd be awesome. Thanks!

Maclaurin series for $\frac{1}{1-x} = 1 + x + x^2 + x^3 + ...$

so ...

$\frac{1}{1+x} = \frac{1}{1-(-x)} = 1 - x + x^2 - x^3 + ...$

integrate ...

$f(x) = \ln(1+x) = C + x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + ...$

since $f(0) = 0$ , $C = 0$

$f(x) = \ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + ...$

$f(x^4) = \ln(1+x^4) = x^4 - \frac{x^8}{2} + \frac{x^{12}}{3} - \frac{x^{16}}{4} + ...$

**CainAndrews** · March 24th 2012, 05:58 PM

You're a saint. THANK YOU!

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