How would you go about proving the following statement
Would you use strong induction ?? Could one explain how ?
I don't think that induction is needed for this problem. I would prove it as follows:
Suppose that x is in N, and that k is a number satisfying 2<=k<=x.
Then, x+k<=x+x=2x<=kx as required.
The first inequatlity follows from the fact that k<=x and the last inequality follows from the fact that 2<=k.
Hope this helps!