TITLE: Sum of 1 + 1/2 + 1/3 +.... + 1/n
QUESTION [10 upvotes]: How do I calculate this sum in terms of 'n'?
I know this is a harmonic progression, but I can't find how to calculate the summation of it. Also, is it an expansion of any mathematical function?
1 + 1/2 + 1/3 + 1/4 +.... + 1/n

REPLY [2 votes]: One can write
$$1+\frac12+\frac13+\cdots+\frac1n=\gamma+\psi(n+1)$$
where $\gamma$ is Euler's constant and $\psi$ is the digamma function.
Of course, one reason for creating the digamma function is to make formulae
like this true.