How do you simplify
\[\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\]
or maybe a generalisation, like
\[\sum_{n=1}^{x}\frac{1}{n}?\]
I don't know any way to do this so far. I've tried to split it into partial fractions, but was not able to do it.
**Any form of simplification would be fine.**

## Comments

Sort by:

TopNewestAs x approaches infinity, the sum approaches infinity. – Daniel Leong · 2 years, 8 months ago

Log in to reply

There is no closed formula for your sum. You can find more information here: http://en.wikipedia.org/wiki/Harmonic_number – Jon Haussmann · 2 years, 9 months ago

Log in to reply

Is not possible to obtain a closed formula using elementary functions, maybe this link will help you: link – Jorge Tipe · 2 years, 9 months ago

Log in to reply