Sequences and series

The topic is divided into the following subtopics:

Introduction to sequences
Arithmetic sequences
Geometric sequences
Limit of a sequence
Infinite series

Introduction to sequences

Part I:

Ways to specify a sequence
Finding of one or more members of a sequence

Part II:

Defining a sequence (nth term formula or recurrent relation)
Properties of sequences (strictly increasing or strictly decreasing, nonincreasing, nondecreasing, upper or lower bounded, bounded)
Finding the nth term of a sequence

Part III:

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Arithmetic sequences

Part I:

Defining a sequence (nth term formula or recurrent relation)
Finding the nth term of a sequence
Finding the common difference of a sequence

Part II:

Finding the nth term of a sequence – complex problems
Finding the common difference of a sequence – complex problems
Sum of the first n terms of a sequence
Systems of equations containing sequence terms

Part III:

Word problems
Equations and inequalities containing sums of sequences

Geometric sequences

Part I:

Defining a sequence (nth term formula or recurrent relation)
Finding the nth term of a sequence
Finding the common ratio of a sequence

Part II:

Finding the nth term of a sequence – complex problems
Finding the common ratio of a sequence – complex problems
Sum of the first n terms of a sequence
Systems of equations containing sequence terms

Part III:

Word problems
Combinations of arithmetic and geometric sequences

Limit of a sequence

Part I:

Evaluation of limits of sequences containing polynomials and rational expressions
Limit laws – sum of limits, difference of limits, product of limits and ratio of limits laws

Part II:

Evaluation of limits with trigonometric, exponential and logarithmic functions

Part III:

Use of the limit of the sequence (1+1/n)^n
Evaluation of limits with radicals
Evaluation of limits containing sums of sequences

Infinite series

Part I:

Summation notation
Finding of the first term and of the common ratio of a geometric sequence
The sum of an infinite geometric series

Part II:

Periodic numbers (repeating decimals)
Finding of all x for which a series diverges or converges
Solving equations with infinite series
Word problems

Part III:

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