The Geometric Series

  • Geometric sequences
  1. \rhd Introduction to geometric sequences (10:44) Recognizing a geometric sequence, the initial term and common ratio.
  2. \rhd Introduction to geometric sequences (advanced) (6:38) An emphasis on the notation is given to deduce the n^{\mathrm{th}} term of the sequence.
  3. \rhd Explicit and recursive formulas for geometric sequences (5:37) Find explicit and recursive formulas for the n^{\mathrm{th}} term of the sequence \{168, 84, 42, 21, \dots\}.
  4. * Practice: Explicit formulas for geometric series. (4 problems)
  • Geometric series
  1. \rhd Introduction to geometric series (6:16) Using a savings account as an application of geometric series.
  2. \rhd Geometric series (2:52) Using the sigma notation to represent the sum of the terms of the sequence.
  3. \rhd Finite geometric series (7:14) Deriving a formula for a finite geometric series.
  4. \rhd Evaluate a finite geometric series (6:54)
    1. Find the sum of the first 50 terms in the sequence: 1+\dfrac{10}{11} + \dfrac{100}{121}+\cdots.
    2. Evaluate 1-0.99+0.99^2-0.99^3+\cdots -0.99^{79}.
    3. Find the sum of the first 30 terms in the sequence given by a_1=10 and a_i = a_{i-1}\dfrac{9}{10}.
  5. * Practice: Geometric series formula. (4 problems)