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wu :: forums    riddles    putnam exam (pure math) (Moderators: SMQ, towr, Icarus, Grimbal, Eigenray, william wu)    Rationalization « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Rationalization  (Read 738 times) ThudnBlunder Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Rationalization   « on: Jul 18th, 2007, 4:56pm » Quote Modify Express       1 ---------  as a sum of terms of the form 2q, where q is rational. 2 - 32 IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Barukh Uberpuzzler     Gender: Posts: 2276 Re: Rationalization   « Reply #1 on: Jul 19th, 2007, 11:16am » Quote Modify -.5 - n/6? IP Logged ThudnBlunder Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Rationalization   « Reply #2 on: Jul 19th, 2007, 11:50am » Quote Modify on Jul 19th, 2007, 11:16am, Barukh wrote: -.5 - n/6? Pardon?       IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Eigenray wu::riddles Moderator Uberpuzzler     Gender: Posts: 1948 Re: Rationalization   « Reply #3 on: Jul 19th, 2007, 12:08pm » Quote Modify Ah, geometric series.  And it's easy enough to turn that into a finite sum (which was probably intended):   2-3/6 + 2-4/6 + 2-5/6 + 2-6/6 + 2-7/6 + 2-8/6 + 2-9/6 + ...  = (2-3/6 + 2-4/6 + 2-5/6 + 2-6/6 + 2-7/6 + 2-8/6)(1+1/2+1/4+...)  = 23/6 + 22/6 + 21/6 + 1 + 2-1/6 + 2-2/6.   This is much more elegant than my dull approach:   (a - b)(a - wb)(a - w2b)(-a - b)(-a - wb)(-a - w2b)  = (a3 - b3)(-a3 - b3)  = -a6 + b6  = -4,   where a = 2, b=21/3, w=e2pi i/3. 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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