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Calculating Fibonacci sequence terms from Binet's formula: the explicit Fibonacci formula.
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In this example of an explicit formula for a sequence, we are calculating Fibonacci sequence terms from Binet's formula: the explicit formula for calculating the Fibonacci sequence terms, and we are asked to evaluate Binet's formula for the first four terms of the Fibonacci sequence. We show that the first four terms of the Fibonacci sequence come out as they should, but evaluating just the fourth term in Binet's formula requires cubing two binomials, so things are getting complicated really fast!
Bonus: very quick derivation of the cube of a binomial formula.
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