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The First is:

1. Suppose hat F1=1, F2=1, F3=2, F4=3, F5=5 where Fn is called a Fibonacci number and in general:

Fn=Fn-1+Fn-2 for n>/= 3. Prove that:

F1+F2+F3+...+Fn=(Fn+2)-1

Secondly is:

2. Prove that F1+F2+F5+...+F2n-1=F2n

Any help. I am looking for a proof via induction with a base case and induction step.