Key Terms

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 $\left(\begin{array}{c}n\\ r\end{array}\right)$

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