# Maclaurin Series for a natural logarithm

Find the Maclaurin series and the interval of convergence for $f(x) = \ln(1-7x^9)$

$$\sum_{n=1}^{\infty} (-1)^n \frac{7x^{9n}}{n}$$

but it seems that my homework assignment website will not accept that answer. I also am not sure how to find the interval of convergence. I know that $\ln|1-x|$ converges for $|x| < 1$, but I cannot figure out the interval of convergence for my current problem.

Any help or insight is greatly appreciated! :)

$$\ln(1-x)=-(x+x^2/2+x^3/3+\cdots)$$ doesn't it?
As for the interval of convergence, we would need $$|7x^9|<1$$ which is $$|x|<\left({1\over 7}\right)^{{1\over 9}}$$
• Your series is right for $ln(1-x)$ but I'm still not sure how to write it for $ln(1-7x^9)$. – Christina Apr 7 '14 at 21:41
• Plug in $7x^9$ in place os $x$. – user140943 Apr 7 '14 at 21:46
This may not matter anymore but it doesnt work because you have $$(-1)^n$$. It should be $$(-1)^{2n+1}$$ in order to start off positive instead of negative. I had the same problem and that was the solution. Here was my full answer: $$\frac{(-1)^{2n+1}7^nx^{9n}}{n}$$