1. Give a sentence P(n) depending on a natural number n, such that P(1),P(2),...,P(99) are true but P(100) is false. Make the sentence as simple as possible.
2. Let <a> be a sequence satisfying a1=a2=1 and a_n = 1/2(a_n-1 + 2/(a_n-2)) for n greater than equal 2. Prove that 1 <= a_n <= 2 for all n in the natural numbers