There are three steps to an Inductive Proof.
(1)Show that is true.
. . That is, that the statement is true for .
(2) Assume that is true.
. . That is, assume the statement is true for .
(3) Proof that is true.
. . Use to show that the statement is true for .
(1) Verify .Prove by Induction that:
. . . . . True.
At this point, I write out the statement just to get a look at it.
This is the statement we want to prove, so it's nice to know what it looks like.
(3) Start with
Add to both sides:
The left side is the left side of .
We must show that the right side is the right side of .
The right side is: .
. . . . . There!
We have shown that: .
Therefore: . for all natural numbers .