5. Prove that Fo + F2 + F4 + · . . + F2n = F2n+1 – 1 where Fn is the nth Fibonacci number. 6. Prove that 2" < n! for all n > 4. (Recall, n! = 1 · 2 · 3 · n.) 7. Prove, by mathematical induction, that Fo+F1+F2+• ·+Fn = Fn+2-1, where Fr is the nth Fibonacci number (Fo = 0, F1 = 1 and Fn %3D %3D

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