counting the number of loop runs I have the following loop structure:
for $i_1=1$ to $m$
for $i_2=i_1$ to $m$
$\vdots$
for $i_n=i_{n-1}$ to $m$  
Of course, all indices $i_k$ are integers, and $m$ and $n$ are also positive integers. 
How can I count how many times the inner loop will run?

Since the loop variables are called $i_1,\ldots,i_n$, there are clearly $n$ nested loops.
This is probably not what you were after, but it is the answer, as per "What You Ask For Is What You Get". (Well actually you asked "How can I count ..."; I'll spare you the answer to that.)
