Why is the series \(\sum \frac{-1}{n}\) divergent like the harmonic series?

[haha1234]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[SammyS]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

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

 

[LCKurtz]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

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