MATH II

• Series


  The sum of the terms of a sequence
• Finite series


  Also called partial sum, has an ending
• Finite series examples


  • S1 = 1
  • S2 = 1 + 3 = 4
  • S3 = 1 + 3 + 6 = 10
  • S4 = 1 + 3 + 6 + 10 = 20
  • S5 = 1 + 3 + 6 + 10 + 15 = 35
• Finite series examples 2

  • S2 = 5 + 15 = 20
  • S4 = 5 + 15 + 25 + 35 = 80
  • S6 = 2 + (-6) + 18 + (-54) + 162 + (-486) = -364
• Infinite series


  The sum of the terms of a sequence that goes on forever
• Sigma notation


  A concise way to express a series using the summation symbol Σ
• Sigma notation examples


  • Σ(1/k) from k=1 to 5
  • Σ(k^2) from k=1 to n
  • Σ((-1)^(k+1)*(2k-1)) from k=1 to 4
• Sigma notation allows us to express series concisely