Limits of sequences¶
Part 3 of the lecture notes. Sequences, limits, Euler's number, asymptotic estimates, recursive sequences.
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1. Sequences and limits of sequences
Definition of sequence and properties · Unbounded sets and their suprema/infima · Infinitesimal and infinite sequences · Monotone sequences · …
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2. Computing limits of sequences
Computing limits of sequences
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3. Euler's number
Euler's number … (Napier's constant) · Euler's number in finance
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4. Comparisons and asymptotic estimates
Comparisons and asymptotic estimates
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5. Hierarchies of infinities and the ratio test
Hierarchies of infinities for sequences, part 1 and part 2 · The ratio test theorem · Hierarchies of infinities for sequences, part 3 and part 4
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6. Recursively defined sequences
Recursively defined sequences · Heron's algorithm