Hello, ff4930!

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.

Prove: .

Verify

. . We have: . . . . . . true!

Assume is true: .

We want to show the is true:

. .

Start with

. .

Add to both sides:

. .

Therefore, we have derived

. .

The inductive proof is complete.