This is the homework, and it shouldn't be difficult, but I can't find the proper identity that would help me simplify this sum:
$\sum_{n=0}^m \frac{1}{n+1}\binom{m}{n}$
Through calculating the results, I can see that the simplified version is:
$\frac{2^m-1}{m+1}$
But I don't know how to transform the former into the later. You need not give the complete solution (although, that's welcomed too), but the identities needed for the simplification should suffice.
EDIT:
How I counted: $\frac{m!}{(n+1)!(m-n)!}$ repeated $m$ times while $n$ increases from 0 to $m$. You can also see the code here: http://pastebin.com/RJ9jd966