As we know, there is an asymptotic series for the digamma function when $z>0$ is a real number.
$$
\psi(z)=\ln z+\sum\_{n=1}^{\infty}{\frac{B\_n}{nz^n}}
$$
$B\_n$ is the first Bernoulli numbers.


How to make a proof?



An asymptotic series for the digamma function
We can prove this, using Euler-Maclaurin Formula.
Here is a introduction from Wikipedia.
<http://en.wikipedia.org/wiki/Euler%E2%80%93Maclaurin_formula>


This is a quite easy problem.
To Admin,
You may be able to consider deleting this question, thanks. ^\_^


