In mathematics, the ratio test is a test (or "criterion") for the convergence of a series ∑ n = 1 ∞ {\displaystyle \sum _{n=1}^{\infty }a_{n},} The test · Examples · Proof · Extensions for L = 1 |
13 авг. 2024 г. · In this section we will discuss using the Ratio Test to determine if an infinite series converges absolutely or diverges. The Ratio Test can ... |
| Признак д’Аламбера |  |
При́знак д’Аламбе́ра — признак сходимости числовых рядов, установлен Жаном д’Аламбером в 1768 г.
Если для числового ряда
существует такое число, что, начиная с некоторого номера, выполняется неравенство
то данный ряд абсолютно сходится; если же,... Википедия
Videolar Notice that the Ratio Test considers the ratio of the absolute values of the terms. As you might expect, the Ratio Test thus gives us information about whether ... |
The Ratio Test: If the limit of |a[n+1]/a[n]| is less than 1, then the series (absolutely) converges. If the limit is larger than one, or infinite, then the ... |
The ratio test for series convergence should be used if it is possible to simplify the ratio of consecutive terms in the series. |
20 авг. 2024 г. · The ratio test is particularly useful for series whose terms contain factorials or exponential, where the ratio of terms simplifies the expression. |
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