Example 6: What is the value of k after the following pseudocode has been executed?

k := 0
for i_1 := 1 to n
  for i_2 := to i_1
    .
    .
    .
   for i_m := 1 to i_(m-1)
     k := k + 1

Note that the initial value of k is 0 and that 1 is added to k each time the nested loop is traversed with a sequence of integers i_1, i_2, ..., i_m such that 1 <= i_m <= i_(m-1) <= ... <= i_1 <= n.