2) Consider the sequence of natural numbers: 1, 1, 2, 3, 5, 8, 13, 21, .... This is the famous Fibonacci sequence and the next term in the sequence is obtained by adding the two previous terms. Let Fn stand for the nth Fibonacci number. So, for example, F₁ = 1, F2 = 1, F3 =2, F4 = 3, and so on. Then we can define this sequence by the rules: F₁ = 1, F₂ = 1, and Fn = Fn-1 + Fn-2 Prove that: F₁+F2 +F3 + F4 ++ Fn = Fn+2 -1

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