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!

2. Re: Can somone please explain what they are asking? (Maclaurin Series)

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

so ...

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

integrate ...

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

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

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

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

3. Re: Can somone please explain what they are asking? (Maclaurin Series)

You're a saint. THANK YOU!