Timeline for Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| May 31, 2021 at 17:33 | comment | added | Elias Zamaria | Hmm... I guess my argument does fail. I thought I found a simple explanation. I guess one can argue that the equality still holds in a way when $x = 1$ but that doesn't look like a rigorous argument to me. | |
| May 27, 2021 at 15:28 | comment | added | Andrea | Doesn't your argument run afoul at the second line? When $x=1$, then $\frac{1}{1+x} = \frac12$ but the series $1-1+1-1+1-\cdots$ does not converge. When $x=-1$, then $\frac{1}{1+x}$ is not even defined and the series $1+1+1+1+\cdots$ diverges. | |
| Feb 14, 2021 at 1:19 | review | First posts | |||
| Feb 14, 2021 at 1:32 | |||||
| Feb 14, 2021 at 1:19 | history | answered | Elias Zamaria | CC BY-SA 4.0 |