Discrete.

Please see the attached file for full problem description.

Rabbit Farm

You own a rabbit far. Every week each pair of rabbits has two baby rabbits. However, the baby rabbits first reproduce when they are two weeks old. Initially you have a pair of newborn rabbits. How many pairs you have after n weeks?

Hogatt's Theorem

Prove Hogatt's Theorem: Any integer number can be written as a sum of terms of Fibonacci series. See attached file for full problem description.

Discrete Structures (Recursively Defined Sequences; Basis Definitions; Induction)

The attached sequences are "recursively defined" (for definiton please see attachment). Please answer the questions regarding each sequence. Thank you.

Recursive Definition Sequence

The attached sequence of numbers is recursively defined. Please complete the sequence.