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wu :: forums    riddles    putnam exam (pure math) (Moderators: Eigenray, william wu, towr, SMQ, Grimbal, Icarus)    Floor Summation « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Floor Summation  (Read 8582 times) ThudnBlunder Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Floor Summation   « on: Nov 9th, 2009, 6:00am » Quote Modify Evaluate         81ntanh/10n    n=1 IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Obob Senior Riddler     Gender: Posts: 489 Re: Floor Summation   « Reply #1 on: Nov 9th, 2009, 2:18pm » Quote Modify It's roughly 1 - 2.413 * 10-264.  Are you looking for an actual precise answer, or is the point just that tanh pi is close to 1? « Last Edit: Nov 9th, 2009, 2:50pm by Obob » IP Logged ThudnBlunder Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Floor Summation   « Reply #2 on: Nov 11th, 2009, 3:25am » Quote Modify on Nov 9th, 2009, 2:18pm, Obob wrote: It's roughly 1 - 2.413 * 10-264.  Are you looking for an actual precise answer, or is the point just that tanh pi is close to 1? As I am not expecting an exact answer, perhaps I should have put this elsewhere. The point is that the answer, a transcendental number, requires at least 239 decimal places before we can discover it does not equal 1. And even more if we want to consider rounding errors.   Do you normally sum series to such precision?   IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Obob Senior Riddler     Gender: Posts: 489 Re: Floor Summation   « Reply #3 on: Nov 11th, 2009, 6:10am » Quote Modify I just observed that the first time floor(n tanh pi) != n-1 occurs around n = 267 or so, summed the series 81(n-1)/10^n = 1, and then gave as a rough error estimate an approximation of the difference between the two series.   I guess I'm just saying that there is no reason to use tanh pi except for obfuscation; the real result lurking here is that   limx->1- sum (floor(n x))/10^n = 1, and that the convergence occurs very quickly. IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs => putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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