Ex 1.13 – Structure and Interpretation of Computer Programs

Exercise 1.13 – SICP

We already know that


We also know that

clip_image004[4] where clip_image006[4]

From the hint clip_image008[5] where clip_image010[5]

So clip_image012[5]

So according to the finonacci definition (1)


Using wolfram alpha we can compute


If you plugin the values in the wolfram alpha , you can see that that both expansions at clip_image018[4]are also the same

Edit hmmm, looks like I missed the point of the problem. The real problem was to prove that Fib(n) approx= phi^n / 2 where phi = (1+sqrt(5))/2. I think I’ll have to redo this proof.


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