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**1. The problem statement, all variables and given/known data**

If a

_{0}=1, and a

_{1}=2, and

a

_{n}=(a

_{(n-1)})^2/a

_{n-2}for n>=2,

prove by induction that

**a**for n>=0

_{n}=2^n**2. Relevant equations**

**3. The attempt at a solution**

(B) a

_{0}=1=2^0=1 yes is true

a

_{1}=2=2^1=2 yes is true

(I) a

_{k}=(2

^{k-1})^2/2

^{k-2}=2

^{k}

Is it true that what I solved. It seems very easy.

I started first with a

_{(k+1)}=(a

_{(k+1-1)})^2/a

_{(k+1-2)}=

(2

^{k})^2

^{(k-1)}=2

^{(k+1)}

Please someone help if I am doing something wrong. I will appreciate. Thank you.