Infinite Sequences, Part 2

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• Misc
  • Colloquium
  • “Bodybuilding! ... for Mathematicians” + career reflections
  • Monday March 30, 4:00-5:00 pm
  • Newton 201
  • Julie Croteau ’97, now at Corning Community College
  • Extra credit for summaries
• Questions?
• Sequences
  • Examples
    • a_n = n / (2n-1)
      • First few elements = 1, 2/3, 3/5, ...
      • a₁₀ = 10/19
      • Converge (to what) or diverge?
        • lim_n→∞ a_n
          
    • a_n = (1/n)^1/n
      • First elements = 1, √2/2, etc.
      • Converges?
        
  • Recursive sequences
    • a_n = f( a_n-..., ... )
    • For example, sequence describing how many times you move a disk to solve a Towers of Hanoi puzzle with n disks total
      
• Next
  • Infinite series
  • Read section 10.2 (“Infinite Series”)

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