Prove the following relations among the Fibonacci Numbers holds for any positive integer ?.

# Algebra

The path of a ship can be described by a hyperbolic model centered at the origin, […]

## The path of a ship can be described by a ...

A swimming pool is being drained through a drain at the bottom of the pool, and […]

## A swimming pool is being drained through a drain at ...

John and his friends bought pastels, brushes, and canvases at an art supply store. The table […]

## John and his friends bought pastels, brushes, and canvases at ...

A fence has a total of 500 planks. Sally paints n planks each day. Write an […]

## A fence has a total of 500 planks. Sally paints ...

Three friends bought a present for their teacher. If they received a 15% discount and then […]