Sequences And Summations: Lesson
Lesson 1 of 1
  1. 1
    We see sequences every day. A simple example is the flow of events over time. In mathematics and computer science, a sequence is a list of numbers. Particularly, a sequence of numbers must always b…
  2. 2
    A finite sequence is exactly what it sounds like - an ordered list of numbers that is finite, meaning it has a stopping value. An extensive, uncountable finite sequence also has a stopping value, b…
  3. 3
    An arithmetic sequence (sometimes called a “progression”) is a particular type of sequence that has an initial value, as with all sequences. A proper arithmetic sequence has a common difference, th…
  4. 4
    Much like the arithmetic sequence, a geometric sequence has an initial term. However, a geometric sequence has a common ratio that yields the following number in the geometric sequence when multipl…
  5. 5
    Moving past sequences, we now look at summations. A summation, as the name implies, is the addition of a sequence of numbers. As discussed earlier, sequences are ordered. Summations, which add up …
  6. 6
    We introduce summation notation in detail, a method for providing a compact description of a summation. Summations start somewhere specific and either terminate definitively (finite) or continue wi…
  7. 7
    Short finite summations, or partial sums, are common in computer science. For example, one of the most common uses occurs with loop counters. Here is a Python example: i = 0 while i < 10: i = i …
  8. 8
    This famous arithmetic sequence (progression) problem was supposedly solved by the mathematician Gauss in his childhood. In essence, one solution involves starting at the center of the 100 numbers …
  9. 9
    We use summation rules to simplify our work. Read summation rules carefully; otherwise, it sounds like double talk! Note that we consistently use k as the symbol for a constant. Rule 1: The summ…

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