SIGMA NOTATION, SEQUENCES AND SERIES, AND MATHEMATICAL INDUCTIONS

If a ball is dropped from a certain height on a floor, the ball definitely bounces for several times. The height reach -d by the ball after a bounce must be le- than the previous height. As the result the ball will stop after several bounces. Can you compute the total distance the ball travels from the beginning rung to stop bouncing? Well understanding about sequences and series will help you to solve such kind of problem.

BASIC COMPETENCE:

• Determining the nth term of a sequence and the sum of the first the nth terms of arithmetic and geometric series.

• Using sigma notation in series and mathematical induction in proving.

• Designing mathematical models of problems related to sequences.

• Solving mathematical models of problems related to series and their interpretations.

KEY WORDS:

• Lower Bounds

• Upper Bounds

• Sigma Notations

• Arithmetic Sequences

• Geometric Sequences

• Arithmetic Series

• Geometric Series

• Convergent

• Divergent

• Infinite Geometric Series

MAIN TOPIC:

A. Sigma Notation

B. The Characteristics of Sigma Notation

C. Arithmetic Sequences and Series

D. Geometric Sequences and Series

E. Infinite Geometric Series

F. Mathematical Inductions

In daily life, we often find something or an event that occurs in a certain order or has numerical patterns such as the growth of population in a certain re)n, the change of agriculture production every year, the decay rate of radioactive elements and the splitting of a cell. The problems above are son examples of the applications of numerical sequences and series.

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