My earlier blog about the Fibonacci series gets a lot of hits, so I thought I would write something more, as clearly there is interest.

Once again this is from “Structure and Interpretation of Computer Programs” (available for free here electronically):

Let and . Then .

So .

(1)

(2) Then

(3) Simplifying (2)

(4) Simplifying further – from (1):

(5)

(6) We know that so we can restate (5) as

So (7)

But also and (7) can be restated as

In other words, .

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