# Sequences and Summations

Learn about sequences and summations.

StartSequences And Summations: Lesson

Lesson 1 of 1

- 1We 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…
- 2A 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…
- 3An 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…
- 4Much 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…
- 5Moving 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 …
- 6We 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…
- 7Short 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 …
- 8This 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 …
- 9We 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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