Task 3: Proof by Induction--10 1. Given that F(n) is the nth Fibonacci number prove that F(n)>=(3/2)n-2. Consider the numbers starting from1; i.e. F(1)=1; F(2)=1; F(3)=F(1)+F(2)=2; (5 points) 2. Given a function over positive integers, where F(0)=0; and F(n)=1+F(floor(n/2)). Then show that F(n)=1+floor(log(n)). Here floor(n/2)=(n-1)/2 if n is odd and n/2 if n is even. (5 points)