A sequence z(adsbygoogle = window.adsbygoogle || []).push({}); _{0},z_{1},z_{2},... is defined by letting z_{0}=3, and z_{k}=(z_{k-1})^{2}for all integers k greater than equal to 1. Show that C_{i}=3^{2i}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 Z_{k}= C_{i}. 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.

C_{n+1}=(C_{n})^{2}and

Z_{n+1}=3^{2n+1}=3^{2n(2)}

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

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# More trouble with induction

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