計算機數學

(10%) Fibonacci numbers are defined by $f_n = f_{n-2} + f_{n-1}$ for $n \ge 2$, with the initial values $f_0 = 0$ and $f_1 = 1$, prove $f_0 f_1 + f_1 f_2 + \dots + f_{2n-1} f_{2n} = f_{2n}^2$ by induction.