Generalized Fibonacci proof
1. A sequence of numbers is defined for every .
Prove that there are real numbers and such that for all natural number ,
I just plugged in the numbers and it works, as the problem just asked to find some real numbers. But that turns out to be the Lucas squence. In fact, the general answer states that
I just have no idea how s and t come. http://www.gconsole.com/forum/emo/5c745924.gif
2. A squence is defined as follows
Find a formula for .
Again, the answer is
It looks like I need to apply the formula above, but how? http://www.gconsole.com/forum/emo/4519626a.gif
Thanks a lot!