Sometimes things don't work as simply as you hoped.
Add up the series
± 1 ± ½ ± ⅓ ± ¼ ± ⅕ ± ⅙ ± ...
where you flip independent fair coins to choose each sign. Graph the probability density of the results. Nice! It must be some well-known function, right?
The value of this function at 2 looks like about 1/8. That should be a big clue, right?
Sorry, it's closer to
0.124999999999999999999999999999999999999999764...
🙄
(1/n)
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Is it related to this: https://www.youtube.com/watch?v=851U557j6HE ?
@post - yes, it is. I posted a lot about this last week, summarized here:
https://johncarlosbaez.wordpress.com/2023/01/04/a-curious-integral/