Sequences and Series

  • Arithmetic sequences
  1. \rhd Summation notation (4:26)
    1. Writing 1+2+\cdots+10 using the summation (sigma) notation.
    2. Writing 1+2+\cdots+100 using the summation (sigma) notation.
    3.  Expanding \displaystyle\sum_{i=0}^{50}\pi i^2.
  2. \rhd Introduction to sequences (8:17) For the sequences \{1,4,7,10\} and \{3,7,11,15\ldots\}, the notation used to indicate a term of the sequence and a formula for it are discussed.
  3. \rhd Introduction to arithmetic sequences (7:06) Recognizing arithmetic sequences, the initial term and their common difference.  Explicit and recursive formulas are discussed.
  4. * Practice: Recursive formulas for arithmetic sequences. (4 problems)
  5. * Practice: Extend arithmetic sequences. (4 problems)
  6. * Practice: Explicit formulas for arithmetic sequences. (4 problems)
  7. \rhd Explicit formulas for arithmetic sequences (6:16) Deriving a formula for the sequence \{-100,-50,0,50, \dots\}.
  • Arithmetic series
  1. \rhd Arithmetic series intro (3:55) The sum of the first n terms in the sequence \{1,2,3,\dots\}.
  2. \rhd Arithmetic series formula (7:46) The sum of the first n terms in the sequence \{a, a+d, a+2d,\dots\}.
  3. \rhd Arithmetic series (sigma notation) (7:01) Find \displaystyle\sum_{k=1}^{550}(2k+50).
  4. \rhd Arithmetic series (sum expression) (6:46) Find (-50)+(-44)+(-38)+\dots +2044.
  5. \rhd Arithmetic series (recursive formula) (5:20) Given that a_1=4 and a_i=a_{i-1}+11, find the sum of the first 650 terms of the sequence.
  6. * Practice: Arithmetic series. (4 problems)