The sum of the terms in a sequence is called a series.<\/li>\n\t
A common notation for series is called summation notation, which uses the Greek letter sigma to represent the sum.<\/li>\n\t
The sum of the terms in an arithmetic sequence is called an arithmetic series.<\/li>\n\t
The sum of the first [latex]n[\/latex] terms of an arithmetic series can be found using a formula.<\/li>\n\t
The sum of the terms in a geometric sequence is called a geometric series.<\/li>\n\t
The sum of the first [latex]n[\/latex] terms of a geometric series can be found using a formula.<\/li>\n\t
The sum of an infinite series exists if the series is geometric with [latex]-1<r<1[\/latex].<\/li>\n\t
If the sum of an infinite series exists, it can be found using a formula.<\/li>\n\t
An annuity is an account into which the investor makes a series of regularly scheduled payments. The value of an annuity can be found using geometric series.<\/li>\n<\/ul>
Glossary<\/h2>\n
annuity<\/dt>
an investment in which the purchaser makes a sequence of periodic, equal payments<\/dd><\/dl>
arithmetic series<\/dt>
the sum of the terms in an arithmetic sequence<\/dd><\/dl>
diverge<\/dt>
a series is said to diverge if the sum is not a real number<\/dd><\/dl>
geometric series<\/dt>
the sum of the terms in a geometric sequence<\/dd><\/dl>
index of summation<\/dt>
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<\/dd><\/dl>
infinite series<\/dt>
the sum of the terms in an infinite sequence<\/dd><\/dl>
lower limit of summation<\/dt>
the number used in the explicit formula to find the first term in a series<\/dd><\/dl>
nth partial sum<\/dt>
the sum of the first [latex]n[\/latex] terms of a sequence<\/dd><\/dl>
series<\/dt>
the sum of the terms in a sequence<\/dd><\/dl>
summation notation<\/dt>
a notation for series using the Greek letter sigma; it includes an explicit formula and specifies the first and last terms in the series<\/dd><\/dl>
upper limit of summation<\/dt>
the number used in the explicit formula to find the last term in a series<\/dd><\/dl>\u00a0","rendered":"
Key Equations<\/h2>\n
\n\n
\n
sum of the first [latex]n[\/latex] \nterms of an arithmetic series<\/td>\n
The sum of the terms in a sequence is called a series.<\/li>\n
A common notation for series is called summation notation, which uses the Greek letter sigma to represent the sum.<\/li>\n
The sum of the terms in an arithmetic sequence is called an arithmetic series.<\/li>\n
The sum of the first [latex]n[\/latex] terms of an arithmetic series can be found using a formula.<\/li>\n
The sum of the terms in a geometric sequence is called a geometric series.<\/li>\n
The sum of the first [latex]n[\/latex] terms of a geometric series can be found using a formula.<\/li>\n
The sum of an infinite series exists if the series is geometric with [latex]-1\n
If the sum of an infinite series exists, it can be found using a formula.<\/li>\n
An annuity is an account into which the investor makes a series of regularly scheduled payments. The value of an annuity can be found using geometric series.<\/li>\n<\/ul>\n
Glossary<\/h2>\n
\n
annuity<\/dt>\n
an investment in which the purchaser makes a sequence of periodic, equal payments<\/dd>\n<\/dl>\n
\n
arithmetic series<\/dt>\n
the sum of the terms in an arithmetic sequence<\/dd>\n<\/dl>\n
\n
diverge<\/dt>\n
a series is said to diverge if the sum is not a real number<\/dd>\n<\/dl>\n
\n
geometric series<\/dt>\n
the sum of the terms in a geometric sequence<\/dd>\n<\/dl>\n
\n
index of summation<\/dt>\n
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<\/dd>\n<\/dl>\n
\n
infinite series<\/dt>\n
the sum of the terms in an infinite sequence<\/dd>\n<\/dl>\n
\n
lower limit of summation<\/dt>\n
the number used in the explicit formula to find the first term in a series<\/dd>\n<\/dl>\n
\n
nth partial sum<\/dt>\n
the sum of the first [latex]n[\/latex] terms of a sequence<\/dd>\n<\/dl>\n
\n
series<\/dt>\n
the sum of the terms in a sequence<\/dd>\n<\/dl>\n
\n
summation notation<\/dt>\n
a notation for series using the Greek letter sigma; it includes an explicit formula and specifies the first and last terms in the series<\/dd>\n<\/dl>\n
\n
upper limit of summation<\/dt>\n
the number used in the explicit formula to find the last term in a series<\/dd>\n<\/dl>\n