# More trouble with induction

1. Jun 8, 2005

### johnnyICON

A sequence z0,z1,z2,... is defined by letting z0=3, and zk=(zk-1)2 for all integers k greater than equal to 1. Show that Ci=32i for i greater than or equal to 0.

I wasn't to clear on what it meant by this, so what I have is that I am trying to show that Zk = Ci. Is that correct?

From there, I proved the base case to be true.

Proving n+1 to be true is where I am having problems.
Cn+1=(Cn)2 and
Zn+1=32n+1=32n(2)

I don't see how I can express Cn+1 to be like Zn+1. I'm not even sure if I am understanding the problem correctly. Am I at least going in the right direction? Any hints?

2. Jun 8, 2005

### johnnyICON

Is this to be done using "Strong Induction"
I was using basic mathematical induction.

3. Jun 8, 2005

### matt grime

We dont' know. You're the one that introduced Ci without explaining what it is.

4. Jun 8, 2005

### johnnyICON

Here's how far I've gotten now,
I'm trying to show that Ck+1=32k+1.

By definition,
Ck+1
= (Ck)2
= (32k)2 By the Induction Hypothesis
= (32k(2))
= (32k+1)

Is that correct?

5. Jun 8, 2005

### johnnyICON

The very first sentence is straight from my textbook. I'm guessing Ci is just another way of representing Zk.

6. Jun 8, 2005

### HallsofIvy

Staff Emeritus
"The very first sentence" was "A sequence z0,z1,z2,... is defined by letting z0=3, and zk=(zk-1)2 for all integers k greater than equal to 1." which says nothing about Ci. You can't prove anything about Ci without knowing exactly how it is defined!

7. Jun 8, 2005

### johnnyICON

"A sequence z0,z1,z2,... is defined by letting z0=3, and zk=(zk-1)2 for all integers k greater than equal to 1. Show that Ci=32i for i greater than or equal to 0."

I e-mailed my professor, he said it is supposed to be Zi, not C... I don't know if that helps...

8. Jun 8, 2005

### matt grime

It helps and makes it easy; just do it. And if you can't write saying where you're stuck.

9. Jun 8, 2005

### johnnyICON

I'm still fixated on this. Maybe if I make the Cs Zs instead?