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11.9.1: Key Terms

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    116453
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    Key Terms

    Addition Principle
    if one event can occur in m m ways and a second event with no common outcomes can occur in n n ways, then the first or second event can occur in m+n 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), C(n,r), denoted ( n r ) ( n r )
    binomial expansion
    the result of expanding (x+y) n (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 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,n} {1,2,n} for some positive integer n n
    Fundamental Counting Principle
    if one event can occur in m m ways and a second event can occur in n n ways after the first event has occurred, then the two events can occur in m×n m×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 m ways and a second event can occur in n n ways after the first event has occurred, then the two events can occur in m×n m×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 n
    nth partial sum
    the sum of the first n 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

    11.9.1: Key Terms is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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