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Timeline for Does the following sum converge?

Current License: CC BY-SA 4.0

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Jul 27, 2020 at 2:55 vote accept RyanChan
Jul 25, 2020 at 0:07 comment added RyanChan Thank you. I will first verify whether your method can be used to solve the new question.
Jul 24, 2020 at 19:20 comment added Iosif Pinelis @RyanChen : Your question has been fully answered. If you have further questions then, for more reasons than one, I suggest you post them separately.
Jul 24, 2020 at 15:18 comment added RyanChan Thanks for your answer. A variation of this sum is $\lim_{n\to \infty}\sum_{k=0}^{\lfloor\alpha n \rfloor}C_n^k(-1)^k(1-\frac{k}{\alpha n})^n$. Does this sum converge?
Jul 24, 2020 at 4:52 history edited Iosif Pinelis CC BY-SA 4.0
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Jul 24, 2020 at 4:30 history edited Iosif Pinelis CC BY-SA 4.0
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Jul 24, 2020 at 3:31 history answered Iosif Pinelis CC BY-SA 4.0