# Math Help - Maclaurin series

1. ## Maclaurin series

Left this late, (as usual):
Use known series to obtain the fourth degree Maclaurin series for:
$f(x) = ln(1-2x) + ln(1-x)$

quick help much appreciated!

2. Originally Posted by Dr Zoidburg
Left this late, (as usual):
Use known series to obtain the fourth degree Maclaurin series for:
$f(x) = ln(1-2x) + ln(1-x)$

quick help much appreciated!

It is "known" that $\ln(1-x)=-\sum_{n=0}^{\infty}\frac{x^{n+1}}{n+1}= g(x)$

Then we know that $\ln(1-2x)=g(2x)=-\sum_{n=0}^{\infty}\frac{(2x)^{n+1}}{n+1}$

$f(x)=g(2x)+g(x)=-\sum_{n=0}^{\infty}\frac{(2x)^{n+1}}{n+1}-\sum_{n=0}^{\infty}\frac{(x)^{n+1}}{n+1}=-\sum_{n=0}^{\infty}\frac{[2^n+1][x^{n+1}]}{n+1}$

Now just let n=0,1,2,3,4 to get your taylor polynomial of degree 4.

Good luck.

3. thanks a lot. Really appreciate it.