One-liner mini-challenge [HP-71B]

[Valentin Albillo]

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Hi again, Gerson:

(04-20-2015 04:41 PM)Gerson W. Barbosa Wrote:  Thank you for your ongoing interest in this fascinating subject!

You're welcome. Thanks to you for issuing this particular one-liner mini-challenge, it's indeed a fascinating subject as you say.

Quote:At page 81 of his book Prime Obsession, John Derbyshire says:

"...if you take the trouble to actually work out the sums and add them up, you see that the first ten terms add up to 5.020997899..., the first hundred add up to 18.589603824..., the first thousand add up to 61.801008765..., the first ten thousand to 198.544645449... and so on."

I followed the link but regrettably page 81 is nowhere to be seen, it belongs in a page gap which isn't visualized so I couldn't check the reference.

Quote:But I digress. Back to your very short solution, I would like to point out I get your exact result for n = 1, using this series, disregarding the last term: [...] The sixth term doesn't help much for n = 1, [...]

It's an asymptotic series (and thus divergent) so using more terms improves accuracy only up to some point, adding more terms after that actually degrades the precision. This can be seen in your example for x=1, where the first five terms do help while adding yet another one (or more) does not.

Regards.
V.
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