11.9.1: Key Terms

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Key Terms

Addition Principle: if one event can occur in $m$ ways and a second event with no common outcomes can occur in $n$ ways, then the first or second event can occur in $m + n$ ways

annuity: an investment in which the purchaser makes a sequence of periodic, equal payments

arithmetic sequence: a sequence in which the difference between any two consecutive terms is a constant

arithmetic series: the sum of the terms in an arithmetic sequence

binomial coefficient: the number of ways to choose r objects from n objects where order does not matter; equivalent to $C (n, r),$ denoted $(\begin{matrix} n \\ r \end{matrix})$

binomial expansion: the result of expanding ${(x + y)}^{n}$ by multiplying

Binomial Theorem: a formula that can be used to expand any binomial

combination: a selection of objects in which order does not matter

common difference: the difference between any two consecutive terms in an arithmetic sequence

common ratio: the ratio between any two consecutive terms in a geometric sequence

complement of an event: the set of outcomes in the sample space that are not in the event $E$

diverge: a series is said to diverge if the sum is not a real number

event: any subset of a sample space

experiment: an activity with an observable result

explicit formula: a formula that defines each term of a sequence in terms of its position in the sequence

finite sequence: a function whose domain consists of a finite subset of the positive integers ${1, 2, \dots n}$ for some positive integer $n$

Fundamental Counting Principle: if one event can occur in $m$ ways and a second event can occur in $n$ ways after the first event has occurred, then the two events can occur in $m \times n$ ways; also known as the Multiplication Principle

geometric sequence: a sequence in which the ratio of a term to a previous term is a constant

geometric series: the sum of the terms in a geometric sequence

index of summation: in summation notation, the variable used in the explicit formula for the terms of a series and written below the sigma with the lower limit of summation

infinite sequence: a function whose domain is the set of positive integers

infinite series: the sum of the terms in an infinite sequence

lower limit of summation: the number used in the explicit formula to find the first term in a series

Multiplication Principle: if one event can occur in $m$ ways and a second event can occur in $n$ ways after the first event has occurred, then the two events can occur in $m \times n$ ways; also known as the Fundamental Counting Principle

mutually exclusive events: events that have no outcomes in common

n factorial: the product of all the positive integers from 1 to $n$

nth partial sum: the sum of the first $n$ terms of a sequence

nth term of a sequence: a formula for the general term of a sequence

outcomes: the possible results of an experiment

permutation: a selection of objects in which order matters

probability: a number from 0 to 1 indicating the likelihood of an event

probability model: a mathematical description of an experiment listing all possible outcomes and their associated probabilities

recursive formula: a formula that defines each term of a sequence using previous term(s)

sample space: the set of all possible outcomes of an experiment

sequence: a function whose domain is a subset of the positive integers

series: the sum of the terms in a sequence

summation notation: a notation for series using the Greek letter sigma; it includes an explicit formula and specifies the first and last terms in the series

term: a number in a sequence

union of two events: the event that occurs if either or both events occur

upper limit of summation: the number used in the explicit formula to find the last term in a series

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Key Terms