Now, we want to prove that P(k+1) is true. This means we want to prove that the following inequality: holds. We shall prove it by using our assumption:
. Now, we shall use the fact that for any positive a,b such that a<b. How will we use this? -- We know that the minimal value of k is 2, and therefore the minimal value of is 3. Therefore, .
--> , and this is exactly what we were looking to prove: . Therefore P(k+1) is true and we are done.