[Solved]: A puzzle related to nested loops

Problem Detail: 

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.

Asked By : Vishnu Vivek

Answered By : Bartosz Przybylski

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

Best Answer from StackOverflow

Question Source : http://cs.stackexchange.com/questions/7008