Originally Posted by

**akolman** Hello, I have no idea how to show that the following infinite series diverge. I am supposed to compare then to the harmonic series... but I just don't get it.

1. $\displaystyle \sum ^\infty _{n=2} \frac{1}{(\log {n})^k}$

**Hint** $\displaystyle \frac {1}{(\log {n})^k} > \frac {1}{n}$ for a sufficiently large $\displaystyle n$

2. $\displaystyle \sum ^\infty _{n=1} \sin {\frac {1}{n} }$

**Hint** $\displaystyle \sin {\frac {1}{n}} > \frac {1}{2n} $ for a sufficiently large $\displaystyle n$

Thanks in advance.