Fibonacci sequence
The Fibonacci sequence is a sequence of integers in which the first and second term are both equal to 1, and each subsequent term is the sum of the two preceding it. The first few terms are
.
The Fibonacci sequence can be written recursively as .
Contents
[hide]Phi
Ratios between successive terms, , , , , , tend towards the limit phi.
Binet's formula
Binet's formula is an explicit formula used to find any nth term. It is .
Problems
Introductory
Intermediate
- Seven line segments, with lengths no greater than 10 inches, and no shorter than 1 inch, are given. Show that one can choose three of them to represent the sides of a triangle. (Manhattan Mathematical Olympiad 2004)
- A fair coin is to be tossed times. Let , in lowest terms, be the probability that heads never occur on consecutive tosses. Find .
Olympiad
See also
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