5. In 1202, Leonardo Fibonacci posed the following problem: Suppose a particular bread of rabbit breeds one new pair of rabbits each month, except that 1-month-old pair is too young to breed. Suppose further that no rabbit breeds with any other except its paired mate and that rabbits live forever. At 1 month, we have our original pair of rabbits. At 2 months, we still have the single pair. At 3 months we have two pairs (the original and their one pair of offspring). At 4 months we have three pairs (the original pair, one older pair of offspring, and one new pair of offspring). (b) Calculate the first 10 Fibonacci numbers fi, f2 , f3... , f10

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**The Fibonacci Sequence and Rabbit Breeding**

In 1202, Leonardo Fibonacci posed the following problem: Suppose a particular breed of rabbit breeds one new pair of rabbits each month, except that 1-month-old pair is too young to breed. Suppose further that no rabbit breeds with any other except its paired mate and that rabbits live forever. 

- At 1 month, we have our original pair of rabbits. 
- At 2 months, we still have the single pair. 
- At 3 months, we have two pairs (the original and their one pair of offspring). 
- At 4 months, we have three pairs (the original pair, one older pair of offspring, and one new pair of offspring).

---

**Exercise**

Calculate the first 10 Fibonacci numbers \( f_1, f_2, f_3, \ldots, f_{10} \).
Transcribed Image Text:**The Fibonacci Sequence and Rabbit Breeding** In 1202, Leonardo Fibonacci posed the following problem: Suppose a particular breed of rabbit breeds one new pair of rabbits each month, except that 1-month-old pair is too young to breed. Suppose further that no rabbit breeds with any other except its paired mate and that rabbits live forever. - At 1 month, we have our original pair of rabbits. - At 2 months, we still have the single pair. - At 3 months, we have two pairs (the original and their one pair of offspring). - At 4 months, we have three pairs (the original pair, one older pair of offspring, and one new pair of offspring). --- **Exercise** Calculate the first 10 Fibonacci numbers \( f_1, f_2, f_3, \ldots, f_{10} \).
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