Exercise 7.
Prove, by mathematical induction, that \(F_0 + F_1 + F_2 + \cdots + F_{n} = F_{n+2} - 1\text{,}\) where \(F_n\) is the \(n\)th Fibonacci number (\(F_0 = 0\text{,}\) \(F_1 = 1\) and \(F_n = F_{n-1} + F_{n-2}\)).
Prove, by mathematical induction, that \(F_0 + F_1 + F_2 + \cdots + F_{n} = F_{n+2} - 1\text{,}\) where \(F_n\) is the \(n\)th Fibonacci number (\(F_0 = 0\text{,}\) \(F_1 = 1\) and \(F_n = F_{n-1} + F_{n-2}\)).