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Geometric Sequences and Series - HEC

Page 1 of 13 Geometric Sequences AND Series Summary 1. Geometric Sequences .. 2 2. Exercise .. 6 3. Geometric sequence applications to financial mathematics .. 6 4. Vocabulary .. 7 5. Exercises : .. 8 6. Geometric Series .. 8 7. Exercises .. 11 8. Geometric Series applications in financial mathematics .. 12 During the duration of an investment, the value of an investment can vary in function of time. The study of an investment at different dates produces a sequence of values. The market index, for example, represents a random sequence in itself. At some point, you surely must have observed a curve of market tendencies like this one : This curve is merely a visualization of the chronological sequence of values: 10 juin 7542 11 juin 7623 12 juin 7743 13 juin 7471 14 juin 7443 15 juin 7501 Page 2 of 13 This section will cover the study of Sequences and Series . We will particularly study Geometric Sequences and Series since these are the subject of most bank contracts (investments, loans, mortgages).

The sequence <1,2,4,8,16,… = is a geometric sequence with common ratio 2, since each term is obtained from the preceding one by doubling. The sequence 9,3,1,1/3,… = is a geometric sequence with common ratio 1/3. Standard form

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