Problem #WSP-000109

Problems Algebra Sequences Recurrent relations Fibonacci numbers

Problem

What’s $\sum_{i = 0}^{n} F_{i}^{2} = F_{0}^{2} + F_{1}^{2} + F_{2}^{2} + . . . + F_{n - 1}^{2} + F_{n}^{2}$ in terms of just $F_{n}$ and $F_{n + 1}$ ?

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