# Convergence of series

1. Apr 28, 2014

### haha1234

1. The problem statement, all variables and given/known data

I know that the harmonic series is divergent.But why $\frac{-1}{n}$ is also divergent?
I've search for some test to test that, but I could not find a method for negative series.
So how can I prove the series is divergent?

2. Relevant equations

3. The attempt at a solution

2. Apr 28, 2014

### SammyS

Staff Emeritus
$\displaystyle (-1)\cdot\sum_{n=1}^\infty \left(\frac{1}{u}\right)=\sum_{n=1}^\infty \left(-\frac{1}{u}\right)$

3. Apr 28, 2014

### LCKurtz

If the partial sums of $\sum\frac 1 n$ diverge, then so do the partial sums of $\sum -\frac 1 n=-\sum\frac 1 n$.

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