You left out a huge chuck of the first problem . . .
We have the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, ...
. . where: . and: .
Each term is the sum of the preceding two terms.
. . We have: . . . . . . true!
Assume is true: .
We want to show the is true:
Add to both sides:
Therefore, we have derived
The inductive proof is complete.