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- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_2_(Sklar)/09%3A_Sequences_and_Series/9.02%3A_Infinite_SeriesIn this section we define an infinite series and show how series are related to sequences. We also define what it means for a series to converge or diverge. We introduce one of the most important type...In this section we define an infinite series and show how series are related to sequences. We also define what it means for a series to converge or diverge. We introduce one of the most important types of series: the geometric series. We will use geometric series in the next chapter to write certain functions as polynomials with an infinite number of terms. This process is important because it allows us to evaluate, differentiate, and integrate complicated functions by using polynomials.
- https://math.libretexts.org/Bookshelves/Analysis/Complex_Variables_with_Applications_(Orloff)/08%3A_Taylor_and_Laurent_Series/8.01%3A_Geometric_SeriesHaving a detailed understanding of geometric series will enable us to use Cauchy’s integral formula to understand power series representations of analytic functions. We start with the definition:
- https://math.libretexts.org/Courses/Lorain_County_Community_College/Book%3A_Precalculus_Jeffy_Edits_3.75/09%3A_Sequences_and_the_Binomial_Theorem/9.02%3A_Summation_NotationIn the previous section, we introduced sequences and now we shall present notation and theorems concerning the sum of terms of a sequence.
- https://math.libretexts.org/Bookshelves/Differential_Equations/A_First_Course_in_Differential_Equations_for_Scientists_and_Engineers_(Herman)/08%3A_Appendix_Calculus_Review/8.06%3A_Geometric_SeriesGeometric series are fairly common and will be used throughout the book. You should learn to recognize them and work with them.
- https://math.libretexts.org/Courses/Fresno_City_College/Math_3A%3A_College_Algebra_-_Fresno_City_College/09%3A_Sequences_Series_and_the_Binomial_Theorem/9.03%3A_Geometric_Sequences_and_SeriesA geometric sequence, or geometric progression, is a sequence of numbers where each successive number is the product of the previous number and some constant r .
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_III%3A_Series_and_Vector_Calculus/01%3A_Sequences_and_Series/1.05%3A_Alternating_SeriesIn this section we introduce alternating series—those series whose terms alternate in sign. We will show in a later chapter that these series often arise when studying power series. After defining alt...In this section we introduce alternating series—those series whose terms alternate in sign. We will show in a later chapter that these series often arise when studying power series. After defining alternating series, we introduce the alternating series test to determine whether such a series converges.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q3/01%3A_Sequences_and_Series/1.06%3A_Alternating_SeriesIn this section we introduce alternating series—those series whose terms alternate in sign. We will show in a later chapter that these series often arise when studying power series. After defining alt...In this section we introduce alternating series—those series whose terms alternate in sign. We will show in a later chapter that these series often arise when studying power series. After defining alternating series, we introduce the alternating series test to determine whether such a series converges.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_222_Calculus_2/04%3A_Sequences_and_Series/4.02%3A_Infinite_SeriesIn this section we define an infinite series and show how series are related to sequences. We also define what it means for a series to converge or diverge. We introduce one of the most important type...In this section we define an infinite series and show how series are related to sequences. We also define what it means for a series to converge or diverge. We introduce one of the most important types of series: the geometric series. We will use geometric series in the next chapter to write certain functions as polynomials with an infinite number of terms. This process is important because it allows us to evaluate, differentiate, and integrate complicated functions by using polynomials.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q3/01%3A_Sequences_and_Series/1.03%3A_Infinite_SeriesIn this section we define an infinite series and show how series are related to sequences. We also define what it means for a series to converge or diverge. We introduce one of the most important type...In this section we define an infinite series and show how series are related to sequences. We also define what it means for a series to converge or diverge. We introduce one of the most important types of series: the geometric series. We will use geometric series in the next chapter to write certain functions as polynomials with an infinite number of terms. This process is important because it allows us to evaluate, differentiate, and integrate complicated functions by using polynomials.
- https://math.libretexts.org/Courses/Coastline_College/Math_C185%3A_Calculus_II_(Tran)/06%3A_Sequences_and_Series/6.06%3A_Alternating_SeriesIn this section we introduce alternating series—those series whose terms alternate in sign. We will show in a later chapter that these series often arise when studying power series. After defining alt...In this section we introduce alternating series—those series whose terms alternate in sign. We will show in a later chapter that these series often arise when studying power series. After defining alternating series, we introduce the alternating series test to determine whether such a series converges.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_401%3A_Calculus_II_-_Integral_Calculus_Lecture_Notes_(Simpson)/03%3A_Sequences_and_Series/3.05%3A_The_Alternating_Series_TestIn this section we introduce alternating series—those series whose terms alternate in sign. We will show in a later chapter that these series often arise when studying power series. After defining alt...In this section we introduce alternating series—those series whose terms alternate in sign. We will show in a later chapter that these series often arise when studying power series. After defining alternating series, we introduce the alternating series test to determine whether such a series converges.
