{"id":451,"date":"2019-07-15T22:45:10","date_gmt":"2019-07-15T22:45:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebracorequisite\/chapter\/summary-series-and-their-notations\/"},"modified":"2019-07-15T22:45:10","modified_gmt":"2019-07-15T22:45:10","slug":"summary-series-and-their-notations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/chapter\/summary-series-and-their-notations\/","title":{"raw":"Summary: Series and Their Notations","rendered":"Summary: Series and Their Notations"},"content":{"raw":"\n
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 \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>\n
Glossary<\/h2>\nannuity<\/strong> an investment in which the purchaser makes a sequence of periodic, equal payments\n\narithmetic series<\/strong> the sum of the terms in an arithmetic sequence\n\ndiverge<\/strong> a series is said to diverge if the sum is not a real number\n\ngeometric series<\/strong> the sum of the terms in a geometric sequence\n\nindex of summation<\/strong> 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\n\ninfinite series<\/strong> the sum of the terms in an infinite sequence\n\nlower limit of summation<\/strong> the number used in the explicit formula to find the first term in a series\n\nnth partial sum<\/strong> the sum of the first [latex]n[\/latex] terms of a sequence\n\nseries<\/strong> the sum of the terms in a sequence\n\nsummation notation<\/strong> a notation for series using the Greek letter sigma; it includes an explicit formula and specifies the first and last terms in the series\n\nupper limit of summation<\/strong> the number used in the explicit formula to find the last term in a series\n","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
annuity<\/strong> an investment in which the purchaser makes a sequence of periodic, equal payments<\/p>\n
arithmetic series<\/strong> the sum of the terms in an arithmetic sequence<\/p>\n
diverge<\/strong> a series is said to diverge if the sum is not a real number<\/p>\n
geometric series<\/strong> the sum of the terms in a geometric sequence<\/p>\n
index of summation<\/strong> 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<\/p>\n
infinite series<\/strong> the sum of the terms in an infinite sequence<\/p>\n
lower limit of summation<\/strong> the number used in the explicit formula to find the first term in a series<\/p>\n
nth partial sum<\/strong> the sum of the first [latex]n[\/latex] terms of a sequence<\/p>\n
series<\/strong> the sum of the terms in a sequence<\/p>\n
summation notation<\/strong> a notation for series using the Greek letter sigma; it includes an explicit formula and specifies the first and last terms in the series<\/p>\n
upper limit of summation<\/strong> the number used in the explicit formula to find the last term in a series<\/p>\n\n\t\t\t \n\t\t\t