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- https://math.libretexts.org/Courses/Coastline_College/Math_C045%3A_Beginning_and_Intermediate_Algebra_(Tran)/14%3A_Sequences_Series_and_Binomial_Theorem/14.02%3A_Sequences\(\begin{array} {}&{ 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}} \\ {}&{n : 1,2,3,4,5} \\ {\text{We look for a pattern in the terms.}}&{\text { Terms: } 1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}...\(\begin{array} {}&{ 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}} \\ {}&{n : 1,2,3,4,5} \\ {\text{We look for a pattern in the terms.}}&{\text { Terms: } 1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}} \\ {\text{The numerators are all one.}}&{\text { Pattern: } \frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots \frac{1}{n}} \\ {\text{The denominators are the counting numbers from one to five.}}&{\text{The sum written in summation notation}} \\ {}&{1 + \frac{1}{…
- https://math.libretexts.org/Workbench/Intermediate_Algebra_2e_(OpenStax)/12%3A_Sequences_Series_and_Binomial_Theorem/12.02%3A_SequencesInstead of writing the function as f ( x ) = 2 x , f ( x ) = 2 x , we would write it as a n = 2 n . a n = 2 n . The a n a n is the nth term of the sequence, the term in the nth position where n is a v...Instead of writing the function as f ( x ) = 2 x , f ( x ) = 2 x , we would write it as a n = 2 n . a n = 2 n . The a n a n is the nth term of the sequence, the term in the nth position where n is a value in the domain. ∑ i = 1 n a i = a 1 + a 2 + a 3 + a 4 + a 5 + … + a n ∑ i = 1 n a i = a 1 + a 2 + a 3 + a 4 + a 5 + … + a n
- https://math.libretexts.org/Courses/Mission_College/Math_C%3A_Intermediate_Algebra_(Carr)/09%3A_Sequences_and_Series/9.01%3A_Sequences\(\begin{array} {}&{ 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}} \\ {}&{n : 1,2,3,4,5} \\ {\text{We look for a pattern in the terms.}}&{\text { Terms: } 1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}...\(\begin{array} {}&{ 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}} \\ {}&{n : 1,2,3,4,5} \\ {\text{We look for a pattern in the terms.}}&{\text { Terms: } 1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}} \\ {\text{The numerators are all one.}}&{\text { Pattern: } \frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots \frac{1}{n}} \\ {\text{The denominators are the counting numbers from one to five.}}&{\text{The sum written in summation notation}} \\ {}&{1 + \frac{1}{…
