The Fibonacci Sequence

This video (up to time 4:46) reviews the definition of recursively defined sequences and defines the Fibonacci sequence. It denotes the Fibonacci sequence as f₁, f₂, f₃, … whereas in the book the sequence is written as F₁, F₂, F₃, … The second part of the video (from time 4:46 to the end) discusses ratios of consecutive Fibonacci numbers, introduces the meaning of the golden ratio, and gives interesting applications. The Fibonacci ratios are the subject of exercises 34 and 35 in Section 5.6, but solving these exercises requires being able to work with limits from calculus. The golden ratio is discussed in Section 5.8, exercise 24.

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