I am working on an assignment in my calculus class. The first task is:
Given a recursively defined sequence:
a(1) = 2, a(n+1) = (a(n)^2 + 2) / 2a(n)
a) Use induction to prove that a(n) >= 0 for all n
I really don't know where to start. I have used induction to prove properties of sums, but when it comes to sequences, and especially recursive ones, I am blank.
Sorry for my potentially broken english!