Here's the question:

Use induction to prove that for every integer , .

Firstly, I'm confused whether to use the simple induction or the complete induction for this problem. I will try the simple one:

Base case: let and let P(n) be the statement:

" , "

Since I can't use P(1) as the base case so I'll do P(4) in its stead:

Inductive step:

Suppose and P(k) is true. So

Now we consider P(k+1)

What else can be done here to prove the inequality?

any help is appreciated