I've read and studied the first 3 paragraphs from Concrete Mathematics and now I've made the first couple of problems. When I got to the actual homework problems I was lost because I tried to solve the problem the way it was taught to me in the book. After trying to solve it for half a hour I decided to look up the answer. The solution used a method which wasn't explained in the book.
Take a look, the following problem:
Solve the recurrence"
$$Q_{0} = \alpha; \text{ } Q_{1} =\beta;$$ $$Q_{n} = (1+Q_{n-1})/ Q_{n-2}; \text{ for } n>1$$
Additional information:
Assume that: $Q_{n} \neq 0 $ for all $n \geq 0 $ Hint: $$Q_{4}=(1+\alpha)/\beta$$
Here is the solution as given by the book:
$$Q_{2} = (1+\beta)/\alpha;Q_{3} = (1+\alpha+\beta)/\alpha\beta;Q_{4}= (1+\alpha)/\beta; Q_{5}= \alpha; Q_{6}=\beta; \text{ So the sequence is periodic! }$$
This is not explained or demonstrated at all in the paragraphs leading up to the problems.
Now my question is: Can I still reap benefits from reading the book without making the exercises? Because I do understand everything in the text, it's just that the problems are screwy..
Kind Regards,
Cro-Magnon