Timeline for Converges or diverges?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Apr 17, 2023 at 7:58 | comment | added | Валерий Заподовников | In 13.2 mathematica.stackexchange.com/a/261428/82985 is fixed, so you can now IMHO replace ClassicLimit with DiscreteLimit[(1 - Log[n]/n)^(2 n), n -> \[Infinity]] | |
| Aug 24, 2022 at 18:52 | comment | added | Валерий Заподовников | BTW, you cannot use Assumptions on -> variable. It prints a warning even in 13.1 on Limit[(1 - Log[n]/n)^(2 n), n -> ∞, Assumptions -> n ∈ Integers]. That only works on ClassicLimit, but even then DiscreteLimit is better, but not always, see mathematica.stackexchange.com/a/261428/82985 | |
| May 31, 2022 at 23:13 | comment | added | Greg Hurst | I would imagine so. Though I don't know the prerequisites to allow the tag. | |
| May 28, 2022 at 13:19 | comment | added | Валерий Заподовников | Can we have a bug header for this and a separate bug for RaabeTest bug mathematica.stackexchange.com/q/224072/82985? | |
| Dec 19, 2021 at 4:41 | comment | added | Валерий Заподовников | Another example that this hack works on is Cos[n] x^n. It returns false... See mathematica.stackexchange.com/a/215363/82985 | |
| Dec 7, 2021 at 11:44 | comment | added | Валерий Заподовников | Do you have any idea what causes RaabeTest to fail for 1 - Cos[Pi/n]? Limit hack does not work there. I think it cannot confirm it is positive sequence, since that is needed for Raabe. | |
| Dec 7, 2021 at 2:45 | history | edited | Greg Hurst | CC BY-SA 4.0 |
added 41 characters in body
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| S Dec 6, 2021 at 17:57 | history | suggested | Валерий Заподовников | CC BY-SA 4.0 |
the whole logics behind it
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| Dec 6, 2021 at 16:50 | review | Suggested edits | |||
| S Dec 6, 2021 at 17:57 | |||||
| Dec 6, 2021 at 16:06 | history | edited | user64494 | CC BY-SA 4.0 |
deleted 1 character in body
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| Dec 6, 2021 at 16:05 | comment | added | user64494 |
Thank you. BTW, Asymptotics ` ClassicLimit[(1 - Log[n]/n)^(2 n), n -> [Infinity]] returns 0. Indeed, the documentation says SumConvergence was not updated since 2010.
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| Dec 6, 2021 at 15:33 | comment | added | Greg Hurst | ‘SumConvergence’ uses that ‘ClassicLimit’ function instead of ‘Limit’. ‘ClassicLimit’ is returning 1 for that limit and so ‘SumConvergence’ thinks the sum is divergent. Forcing ‘SumConvergence’ to use ‘Limit’ instead of ‘ClassicLimit’ fixes this issue. | |
| Dec 6, 2021 at 14:58 | comment | added | user64494 | The condition $\lim_{n\to\infty}a_n=0$ is only a necessary condition for the convergence of a series. There are both convergent series and divergent series which satisfy it. | |
| Dec 6, 2021 at 14:02 | comment | added | user64494 | Can you kindly elaborate your post to make it understandable? TIA. | |
| Dec 6, 2021 at 13:25 | history | answered | Greg Hurst | CC BY-SA 4.0 |