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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/Under_Construction/Purgatory/Book%3A_Active_Calculus_(Boelkins_et_al.)/08%3A_Sequences_and_Series/8.03%3A_Series_of_Real_NumbersAn infinite series is a sum of the elements in an infinite sequence. The sequence of partial sums of a series P∞ k=1 ak tells us about the convergence or divergence of the series. The series converges...An infinite series is a sum of the elements in an infinite sequence. The sequence of partial sums of a series P∞ k=1 ak tells us about the convergence or divergence of the series. The series converges if the sequence of partial sums 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/Bookshelves/Calculus/Book%3A_Active_Calculus_(Boelkins_et_al.)/08%3A_Sequences_and_Series/8.03%3A_Series_of_Real_NumbersAn infinite series is a sum of the elements in an infinite sequence. The sequence of partial sums of a series P∞ k=1 ak tells us about the convergence or divergence of the series. The series converges...An infinite series is a sum of the elements in an infinite sequence. The sequence of partial sums of a series P∞ k=1 ak tells us about the convergence or divergence of the series. The series converges if the sequence of partial sums converges.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/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/Applied_Mathematics/The_Essence_of_Mathematics_Through_Elementary_Problems_(Borovik_and_Gardiner)/06%3A_Infinity_-_Recursion_Induction_Infinite_Descent/6.06%3A_The_harmonic_series(a) Arrange a stack of n strips of length 2, one on top of the other, with the bottom strip protruding distance 1 n beyond the edge of the table, the second strip from the bottom protruding 1 n − 1 be...(a) Arrange a stack of n strips of length 2, one on top of the other, with the bottom strip protruding distance 1 n beyond the edge of the table, the second strip from the bottom protruding 1 n − 1 beyond the leading edge of the bottom strip, the third strip from the bottom protruding 1 n − 2 beyond the leading edge of the strip below it, and so on until the ( n − 1 ) th strip from the bottom protrudes distance 1 2 beyond the leading edge of the strip below it, and the top strip protrudes dista…
- https://math.libretexts.org/Courses/Mission_College/Mission_College_MAT_003B/05%3A_Sequences_and_Series/5.02%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/Workbench/MAT_2420_Calculus_II/05%3A_Sequences_and_Series/5.03%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/Al_Akhawayn_University/MTH2301_Multivariable_Calculus/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/Courses/Cosumnes_River_College/Math_401%3A_Calculus_II_-_Integral_Calculus_Lecture_Notes_(Simpson)/03%3A_Sequences_and_Series/3.02%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.
