Sequences and Probability:
The sequence is a function whose domain is natural numbers. Rather than using the f(x) notation, though, a sequence is listed by using a notation. There are infinite sequences whose domain is the set of all the positive integers, and there are limited sequences whose domain is the set of first n positive integers.
Whenever you define a sequence, you should write the general term (nth term or an). There is sometimes more than one sequence which is possible when merely the first few terms are given.Probability: It is a chance that an event will take place. Theoretically for equally likely events, this is the number of ways an event can take place divided by number of outcomes in sample space. Empirically, it is the long term relative frequency.Basic Definitions:
Experiment: Any happening whose outcome or result is uncertain.
Outcomes: Possible outcomes/results from an experiment.
Sample Space: It is the set of all possible outcomes.
Event: It is the subset of sample space. There will be one or more outcomes.Key topics included in this chapter are as follows:
a) Sequences and Summation Notationb) Arithmetic Sequencesc) Geometric Sequencesd) Mathematical Inductione) The Binomial Theoremf) ounting Principlesg) Probability
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