`(x/y)^(n + 1) = 1 and 0

You need to use mathematical induction to prove the inequality, hence, you need to perform the following two steps, such that:

Step 1: Basis: Prove that the statement holds for n = 1

If x<y then `(x/y)^2 <= (x/y)^1` holds

Step 2: Inductive step: Show that if P(k) holds, then also P(k + 1) holds.

`P(k): (x/y)^(k+1) <= (x/y)^k` holds

`P(k+1): (x/y)^(k+2) <= (x/y)^(k+1) `

`(x/y)^(k+1)*(x/y) <= (x/y)^(k+1) => x/y <= 1 => x <= y` true

Hence, since both the basis and the inductive step hold, the statement `P(n): (x/y)^(n+1) <= (x/y)^n` holds for all indicated values of n.