Trying to understand how rearrangements work. A very common example of rearrangements seems to be the alternating harmonic series,

$$\sum \_{n=1}^{\infty} \frac {(-1)^{n+1}}{n}$$

Plugging in values of $n$ gives, 

$$1-\frac{1}{2}+\frac {1}{3}-....$$ and so on. How can I rearrange this sum so that the first $10$ sum to $0$.

It seems that I must alter it in some way grouping together positive and negative terms so that the first 10 terms sum to 0.