This requires some work to write down carefully, but it's not too hard. See this thread for some references.
here's another problem for the strong induction.
Prove that for all
so the goal is
let n be arbitrary in N. Suppose
and since we have to prove P(n), also suppose
I proved some base cases for n=1,2.so let's consider the case
so using inductive hypothesis,
but after this point, I got stuck. I can see that, using recurrence
relation for the Fibonacci numbers
can people give some hints ?