jasperE3 wrote: The (Fibonacci) sequence $f_n$ is defined by $f_1=f_2=1$ and $f_{n+2}=f_{n+1}+f_n$ for $n\ge1$. Prove that the area of the triangle with the sides $\sqrt{f_{2n+1}},\sqrt{f_{2n+2}},$ and $\sqrt{f_{2n+3}}$ is equal to $\frac12$. It's not true... maybe there's typo. Since $\sqrt{f_{2n+1}}^2 + \sqrt{f_{2n+2}}^2 = \sqrt{f_{2n+3}}^2$, this triangle is right angled. Hence the area is $\frac{1}{2} \sqrt{f_{2n+1}f_{2n+2}}$.