enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Alternating series test - Wikipedia

    en.wikipedia.org/wiki/Alternating_series_test

    In mathematical analysis, the alternating series test is the method used to show that an alternating series is convergent when its terms (1) decrease in absolute value, and (2) approach zero in the limit.

  3. Harmonic series (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Harmonic_series_(mathematics)

    The series = + = + + is known as the alternating harmonic series. It is conditionally convergent by the alternating series test , but not absolutely convergent . Its sum is the natural logarithm of 2 .

  4. Alternating series - Wikipedia

    en.wikipedia.org/wiki/Alternating_series

    Like any series, an alternating series is a convergent series if and only if the sequence of partial sums of the series converges to a limit. The alternating series test guarantees that an alternating series is convergent if the terms a n converge to 0 monotonically, but this condition is not necessary for convergence.

  5. Riemann series theorem - Wikipedia

    en.wikipedia.org/wiki/Riemann_series_theorem

    Suppose that two positive integers a and b are given, and that a rearrangement of the alternating harmonic series is formed by taking, in order, a positive terms from the alternating harmonic series, followed by b negative terms, and repeating this pattern at infinity (the alternating series itself corresponds to a = b = 1, the example in the ...

  6. Absolute convergence - Wikipedia

    en.wikipedia.org/wiki/Absolute_convergence

    If a series is convergent but not absolutely convergent, it is called conditionally convergent. An example of a conditionally convergent series is the alternating harmonic series. Many standard tests for divergence and convergence, most notably including the ratio test and the root test, demonstrate absolute convergence.

  7. 1 + 2 + 3 + 4 + ⋯ - ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E...

    Those methods work on oscillating divergent series, but they cannot produce a finite answer for a series that diverges to +∞. [6] Most of the more elementary definitions of the sum of a divergent series are stable and linear, and any method that is both stable and linear cannot sum 1 + 2 + 3 + ⋯ to a finite value (see § Heuristics below).

  8. Series (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Series_(mathematics)

    A famous example of an application of this test is the alternating harmonic series = + = + +, which is convergent per the alternating series test (and its sum is equal to ⁡), though the series formed by taking the absolute value of each term is the ordinary harmonic series, which is divergent.

  9. 1/2 + 1/4 + 1/8 + 1/16 + ⋯ - ⋯ - Wikipedia

    en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/...

    The geometric series on the real line. In mathematics, the infinite series1 / 2 ⁠ + ⁠ 1 / 4 ⁠ + ⁠ 1 / 8 ⁠ + ⁠ 1 / 16 ⁠ + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation, this may be expressed as