MathNet 1997 — Part 01 Question 1

Let $F_n$ be the Fibonacci sequence $F_1 = F_2 = 1$, $F_{n+2} = F_{n+1} + F_n$. Put $V_n = \sqrt{F_n^2 + F_{n+2}^2}$. Show that $V_n$, $V_{n+1}$, $V_{n+2}$ are the sides of a triangle of area $1/2$.