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Arew
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Homework Statement
Use iteration to guess an explicit formula for u_k = u_{k−2} * u_{k−1}, for all integers k ≥ 2, u_0 = u_1 = 2 and prove it .
Homework Equations
Hint: Express the answer using the Fibonacci sequence.
The Attempt at a Solution
u_k = u_{k−2} * u_{k−1} and u_0 = u_1 = 2, so
u_2 = 2^2
u_3 = 2^3
u_4 = 2^5
u_5 = 2^8
u_6 = 2^13
u_7 = 2^21
Then (I think) in general we have ,
2^{F_k} = 2^{F_k-1 + F_k-2}
Not finished yet... But does it make sense so far?
BTW, I tried putting $ signs around expressions, but mathjax(?) doesn't seem to render in preview. [/B]