# Closed form of harmonic series

1. Oct 31, 2012

### Dansuer

HI!

I was wandering if there is a proof that the harmonic sum $\sum\frac{1}{k}$ has no closed form. Something like the proof that an equation with degree more than 4 has no solution in terms of radicals.

2. Oct 31, 2012

### Erland

This series diverges to infinity.

3. Oct 31, 2012

### Dansuer

yeah that's cool but that's not what i'm looking for. Maybe i've not been very clear.
I'll try again.

There is not a closed form expression of the harmonic sum $\sum^{n}_{0}\frac{1}{k}$. which means it cannot be expressed in terms of elementary functions (e^x,sin(n), log(n), ...).
This is a closed form for $\sum^{n}_{0} k$

$\sum^{n}_{0} k = \frac{n(n+1)}{2}$

Does a closed form exist, but it's not yet been found ?
or it had been proved that it cannot exist ?
or maybe there is, maybe not, nobody knows anything about it ?