Infinite Sequences and Series · Medium problem

For how many integers $p$ with $1\le p\le10$ does $\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^n}{n^p}$ converge even though $\displaystyle\sum_{n=1}^{\infty}\frac1{n^p}$ (the series of absolute values) diverges?