I need to calculate the following series 

$$\sum\_{k=1}^\infty \frac{(-1)^k \cdot x^k}{3^k\*k}$$

This is what I've done, and for some reason its wrong.

$$\sum\_{k=1}^\infty (-1)^k\cdot\frac{x^k}{3^k\cdot k} =$$
$$\sum\_{k=0}^\infty (-1)^{k+1}\cdot \frac{x^{k+1}}{3^{k+1}\cdot (k+1)} =$$
$$-\sum\_{k=0}^\infty (-1)^{k}\cdot \frac{x^{k+1}}{3^{k+1}\cdot (k+1)} =$$
$$-\sum\_{k=0}^\infty (-1)^{k}\cdot \frac{(\frac{x}{3})^{k+1}}{(k+1)} =$$
$$-\ln(1+\frac{x}{3})$$

I don't understand what's wrong with my answer? Any ideas?

Any help will be appreciated.