Let F: N->N be defined by f(1)=1 and f(2)=2 and f(n+2)=1/2(f(n+1)+f(n))
Use Theorem 1.3 to prove that 1<=f(n)<=2 for all n in N
For each n in N let P(n) be a statement about the positive integer n. If a) P(1) is true, and b) for k>1, P(k) is true whenever P(j) is true for all positive integers j<k, then P(n) is true for all n in N.
The Attempt at a Solution
I honestly don't really know how to even start this one. I have a hard time understanding what the theorem is even saying, so I don't know how to apply it.