Hello, Sarah!

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.

(2) Assume

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.

Replace with

(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 .