Recurrence relations

• How Many Ways Can You Climb n Stairs Using 2 or 3 at a Time?
  Count ways to climb n stairs using only 2- or 3-stair moves: derive the recurrence, generating function, and an explicit binomial-sum formula.
• How to Approach a Difficult Sequence Problem
  A sequence problem needs a definition; use patterns only to form conjectures, then prove them with induction, monotonicity, bounds, or recurrence limits.