Let \(\{F_n\}\) be the Fibonacci sequence: \(F_0=1, F_1=1\) and \(F_n=F_n+F_{n-1}\) for \(n\geq 2\). Show that
\[\sum_{i=0}^n (n-i)F_i=F_{n+3}-n-3\]

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yes, sorry it's a typo :\(F_n=F_{n-1}+F_{n-2}\)

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