本题目来源于试卷: Proofs Proofs ，类别为 IB数学
[问答题]
The Fibonacci sequence pm(mva: wjz9-yrl5den u9kdz7 ,+a u;is9kxn wl72*k(j.a oj fk defined as follows:
$\begin{array}{l}
a_{0}=0, a_{1}=1, a_{2}=1 \\
a_{n}=a_{n-1}+a_{n-2} \text { for } n \geq 2 .(F S)
\end{array}$
Prove by mathematical induction that $a_{1}^{2}+a_{2}^{2}+\cdots+a_{n}^{2}=a_{n} a_{n+1}$ , where $n \in \mathbb{Z}^{+}$ .
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