Question

What is the value of k after the following code has been executed?
k := 0
for i1 := 1 to n1
for i2 := 1 to n2
.
.
.
for im := 1 to nm
k := k + 1

Answer 1

The value of k would be $k=\sum\limits_{i_1=1}^{n_1} \sum\limits_{i_2=1}^{n_2}...\sum\limits_{i_m=1}^{n_m}1$ =$\sum\limits_{i_1=1}^{n_1} \sum\limits_{i_2=1}^{n_2}...\sum\limits_{i_{m-1}=1}^{n_{m-1}}n_m$ =$\sum\limits_{i_1=1}^{n_1} \sum\limits_{i_2=1}^{n_2}...\sum\limits_{i_{m-2}=1}^{n_{m-2}}n_m \cdot n_{m-1}=$$=...=\prod\limits_{i=1}^{m}n_i$