A puzzle related to nested loops For a given input $N$, how many times does the enclosed statement executes?


  for $i$ in $1\ldots N$ loop 
  $\quad$for $j$ in $1\ldots i$ loop 
  $\quad$$\quad$for $k$ in $i\ldots j$ loop 
  $\quad$$\quad$$\quad$$sum = sum + i$ ; 
  $\quad$$\quad$end loop; 
  $\quad$end loop; 
  end loop; 


Can anyone figure out an easy way or a formula to do this in general. Please explain.
You need to solve simple formula

$\sum_{i=1}^N\sum_{j=1}^i\sum_{k=i}^j1$

this will give you overall result of

$\frac{1}{6}N(N+1)(N+2)$

Math is easy to do here but I used Wolfram Alpha