Understanding How Many Times Nested Loops Will Run

Question

I am trying to understand how many times the statement \"x = x + 1\" is executed in the code below, as a function of \"n\":

for (i=1; i<=n; i++)
  for (j=1; j         


        

Answer 1

This number is equal to the number of triples {a,b,c} where a<=b<=c<=n.
Therefore it can be expressed as a Combination with repetitions.. In this case the total number of combinations with repetitions is: n(n+1)(n+2)/6