# I Sum of harmonic progression

1. Oct 25, 2016

### parshyaa

2. Oct 25, 2016

### Staff: Mentor

Do you mean the phrase:

3. Oct 25, 2016

### parshyaa

Yes

4. Oct 25, 2016

### Staff: Mentor

5. Oct 29, 2016

### parshyaa

I think this video makes every thing clearer, thanks jedishrfu

6. Oct 29, 2016

### parshyaa

Still i don't have any clue/answer for why there is no formula for sum of HP for n terms, and i am not able to open your link

7. Oct 29, 2016

### Igael

Are you asking why there is not a smart formula for the exact sum with k from 0 to n ? The wiki page speaks mainly of integer sum and the clever video of divergence and infinite sum, which are another things.

8. Oct 29, 2016

### Svein

As n grows large, you have $\sum_{k=1}^{n}\frac{1}{k}\approx \ln(n)+\gamma$.

9. Oct 29, 2016

### Igael

there is a nice but not very useful formula :
$\sum_{k=1}^{n}{\frac{1}{{a}+{b k}}}=\frac{{\psi^{(0)}({{\frac{a}{b}}+{n}}+{1})}-{\psi^{(0)}({\frac{a}{b}}+{1})}}{b}$ where $\psi^{(n)}(u)$ is the polygamma function

10. Oct 30, 2016

Yes