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  2. Direct comparison test - Wikipedia

    en.wikipedia.org/wiki/Direct_comparison_test

    In mathematics, the comparison test, sometimes called the direct comparison test to distinguish it from similar related tests (especially the limit comparison test), provides a way of deducing whether an infinite series or an improper integral converges or diverges by comparing the series or integral to one whose convergence properties are known.

  3. Limit comparison test - Wikipedia

    en.wikipedia.org/wiki/Limit_comparison_test

    Download QR code; Print/export Download as PDF; Printable version; In other projects ... That is, both series converge or both series diverge.

  4. Modes of convergence - Wikipedia

    en.wikipedia.org/wiki/Modes_of_convergence

    In a topological abelian group, convergence of a series is defined as convergence of the sequence of partial sums. An important concept when considering series is unconditional convergence, which guarantees that the limit of the series is invariant under permutations of the summands.

  5. Divergent series - Wikipedia

    en.wikipedia.org/wiki/Divergent_series

    The two classical summation methods for series, ordinary convergence and absolute convergence, define the sum as a limit of certain partial sums. These are included only for completeness; strictly speaking they are not true summation methods for divergent series since, by definition, a series is divergent only if these methods do not work.

  6. Convergent series - Wikipedia

    en.wikipedia.org/wiki/Convergent_series

    In mathematics, a series is the sum of the terms of an infinite sequence of numbers. More precisely, an infinite sequence (,,, …) defines a series S that is denoted = + + + = =. The n th partial sum S n is the sum of the first n terms of the sequence; that is,

  7. Alternating series - Wikipedia

    en.wikipedia.org/wiki/Alternating_series

    The theorem known as the "Leibniz Test" or the alternating series test states that an alternating series will converge if the terms a n converge to 0 monotonically. Proof: Suppose the sequence a n {\displaystyle a_{n}} converges to zero and is monotone decreasing.

  8. 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.

  9. Microsoft Excel - Wikipedia

    en.wikipedia.org/wiki/Microsoft_Excel

    Excel for the web is a free lightweight version of Microsoft Excel available as part of Office on the web, which also includes web versions of Microsoft Word and Microsoft PowerPoint. Excel for the web can display most of the features available in the desktop versions of Excel, although it may not be able to insert or edit them.