From the course: Programming Foundations: Discrete Mathematics
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Sequences and sums
From the course: Programming Foundations: Discrete Mathematics
Sequences and sums
- [Voiceover] Sequences and sums. Often, sets contain sequences of numbers. These sequences can be finite, or infinite. A finite sequence has an initial index value of m, and a final index value, n, which must be greater than or equal to m. The value of m starts with one and goes to n. I want to point out that this represents the placeholder for the number in the sequence, it is not related to the actual value of the number in the sequence. It is often helpful to define a sequence using an explicit formula showing how term a-sub-k depends on the position in the sequence denoted by the value, k. Given this sequence, two to the first, two-squared, two-cubed, we want to consider an explicit forumla for this series. If you look at the first element in the list, it's two raised to the first power. The second element is two raised to the second power, et cetera. We can represent each element in this series as d-sub-k, meaning the element in the list in the k's position is equal to two…
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Contents
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Objects as sets2m 56s
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Set notation3m 56s
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Set operations5m 1s
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Power sets4m 29s
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Sequences and sums7m 22s
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Recursion3m 5s
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Cardinality, disjointness, and partitions2m 19s
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Sets from Cartesian products3m 2s
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Challenge: Practice with sets47s
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Solution: Practice with sets6m 53s
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