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  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. Convergence tests - Wikipedia

    en.wikipedia.org/wiki/Convergence_tests

    If r > 1, then the series diverges. If r = 1, the root test is inconclusive, and the series may converge or diverge. The root test is stronger than the ratio test: whenever the ratio test determines the convergence or divergence of an infinite series, the root test does too, but not conversely. [1]

  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

    The alternating harmonic series is a classic example of a conditionally convergent series: = + is convergent, whereas = | + | = = is the ordinary harmonic series, which diverges. Although in standard presentation the alternating harmonic series converges to ln(2) , its terms can be arranged to converge to any number, or even to diverge.

  6. 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 .

  7. Integral test for convergence - Wikipedia

    en.wikipedia.org/wiki/Integral_test_for_convergence

    The integral test applied to the harmonic series. Since the area under the curve y = 1/ x for x ∈ [1, ∞) is infinite, the total area of the rectangles must be infinite as well. Part of a series of articles about

  8. 30 Of The Funniest Black Friday Memes To Check Out ... - AOL

    www.aol.com/90-funny-relatable-black-friday...

    Image credits: suburbanbeard While that 0.6% increase might not sound like a lot of money, any additional cash you can choose how you spend is valuable. Meanwhile, after-tax income, adjusted for ...

  9. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.