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  2. Convergence tests - Wikipedia

    en.wikipedia.org/wiki/Convergence_tests

    If the limit of the summand is undefined or nonzero, that is , then the series must diverge. In this sense, the partial sums are Cauchy only if this limit exists and is equal to zero. The test is inconclusive if the limit of the summand is zero.

  3. nth-term test - Wikipedia

    en.wikipedia.org/wiki/Nth-term_test

    In mathematics, the nth-term test for divergence [1] is a simple test for the divergence of an infinite series: If lim n → ∞ a n ≠ 0 {\displaystyle \lim _{n\to \infty }a_{n}\neq 0} or if the limit does not exist, then ∑ n = 1 ∞ a n {\displaystyle \sum _{n=1}^{\infty }a_{n}} diverges.

  4. Limit comparison test - Wikipedia

    en.wikipedia.org/wiki/Limit_comparison_test

    In mathematics, the limit comparison test (LCT) (in contrast with the related direct comparison test) is a method of testing for the convergence of an infinite series. Statement [ edit ]

  5. Ratio test - Wikipedia

    en.wikipedia.org/wiki/Ratio_test

    In mathematics, the ratio test is a test (or "criterion") for the convergence of a series =, where each term is a real or complex number and a n is nonzero when n is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test.

  6. Summation - Wikipedia

    en.wikipedia.org/wiki/Summation

    Summation of a sequence of only one summand results in the summand itself. Summation of an empty sequence (a sequence with no elements), by convention, results in 0. Very often, the elements of a sequence are defined, through a regular pattern, as a function of their place in the sequence. For simple patterns, summation of long sequences may be ...

  7. 5 Things to Avoid When You Have Alopecia Areata - AOL

    www.aol.com/5-things-avoid-alopecia-areata...

    4. Not Enough Vitamin D. You shouldn’t get too much sun, but some vitamin D exposure is essential.A review of studies found that people with certain autoimmune diseases may have a vitamin D ...

  8. Some tax refunds can come with hidden fees, government report ...

    www.aol.com/tax-refunds-come-hidden-fees...

    Further, many taxpayers qualify for free assistance from preparers certified by the IRS. "Many taxpayers get their refunds from the IRS in 10 to 21 days," the CFPB advises. "Waiting a week or two ...

  9. Monotone convergence theorem - Wikipedia

    en.wikipedia.org/wiki/Monotone_convergence_theorem

    The theorem states that if you have an infinite matrix of non-negative real numbers , such that the rows are weakly increasing and each is bounded , where the bounds are summable < then, for each column, the non decreasing column sums , are bounded hence convergent, and the limit of the column sums is equal to the sum of the "limit column ...