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Sequences, Series, Finance
CHAPTER 1
Chapter 1: Sequences, Series, Finance
• Content:
– Introduction
– Sequences
• Basic definitions
• Limit of a sequence
– Series
• Partial sums
• Series and convergence of series
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Chapter 1: Sequences, Series, Finance
• Content-continued
– Finance
• Simple interest and compound interest
• Periodic payments
• Loan repayments, redemption tables
• Investment projects
• Depreciation
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1. Introduction
• Sequences and Series play important roles in business applications
• Several finance problems are approached through sequences and series
• This chapter will treat some of these topics
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SEQUENCES CHO1- PART1
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2. Sequences and Series-Basic Definitions
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Reminder
• ℕ refers to the set of all natural numbers.
• There is no agreement about whether to include zero in the set of natural numbers: – some define the natural numbers to be
the positive integers {1, 2, 3, ...}, • Notations:
– while for others the term designates the non-negative integers {0, 1, 2, 3, ...}. • Notations:
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2. Sequences and Series-Basic Definitions
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2. Sequences and Series-Illustrative examples
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2. Sequences and Series-Illustrative examples
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2. Sequences and Series-Illustrative examples
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Arithmetic and Geometric Sequences
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Arithmetic and Geometric Sequences
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Arithmetic and Geometric Sequences
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Arithmetic and Geometric Sequences
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Arithmetic and Geometric Sequences
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Arithmetic and Geometric Sequences
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Arithmetic and Geometric Sequences
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Arithmetic and Geometric Sequences
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Under these assumptions, what would be the year where the firm’s production first exceeds 55,000 DVD players?
Arithmetic and Geometric Sequences
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Arithmetic and Geometric Sequences
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Increasing/Decreasing Sequences
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Monotone Sequences
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Monotone Sequences
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Monotone Sequences
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Monotone Sequences
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Monotone Sequences
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Monotone Sequences
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Monotone Sequences
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Bounded Sequences
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Monotone Sequences
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Monotone Sequences
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Monotone Sequences
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Monotone Sequences
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Monotone Sequences
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Limit of a sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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The terms of the sequence {an} tend to number 1.
Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
• The definition of a limit is not appropriate for determining its value.
• It can be used to confirm that some guessed value a is in fact the limit of a certain sequence.
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence
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Limit of a Sequence-Example 2.10-continued
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Limit of a Sequence-Example 2.10-continued
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Limit of a Sequence-Example 2.10-continued
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Limit of a Sequence-Example 2.10-continued
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Limit of a Sequence-Example 2.11
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Some Frequently Used Limits
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