‚T‚¿‚á‚ñ‚Ë‚é šƒXƒ}ƒz”Łš ¡ŒfŽ¦”‚ɖ߂遡 ‘S•” 1- ÅV50  

¡ ‚±‚̃XƒŒƒbƒh‚͉ߋŽƒƒO‘qŒÉ‚ÉŠi”[‚³‚ê‚Ä‚¢‚Ü‚·

•s“™Ž®‚ւ̏µ‘Ò ‘æ‚QÍ

1 F•s“™Ž®ƒ’ƒ^F05/01/17 06:40:16
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@@@@@@@@@@QQQ@@@@@@@@@@----- ŽQl•¶Œ£k‚Rl P.65 -----
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@@@@|„«@@ |:::: @_ .^@|@
@@@@|„«@ß|::::: (œ@(œ |@@•s“™Ž®‚Æ•·‚î‚¿‚á‚Ÿ
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@@@@|„«=QQ@@@ _@@@ @@ @@@@ʧʧ
@@@@|„«@ß@j@@l@_ ƒKƒ‰ƒb

•s“™Ž®ƒXƒŒƒbƒh i‘OƒXƒŒj
http://science3.2ch.net/test/read.cgi/math/1072510082/l50

•s“™Ž®‚Ì–{
[1]@•s“™Ž®Aƒn[ƒfƒBEƒŠƒgƒ‹ƒEƒbƒhEƒ|ƒŠƒ„AƒVƒ…ƒvƒŠƒ“ƒK[A2003”N
[2]@•s“™Ž®A‘åŠÖM—YEÂ–؉ëŒvAꠏ‘“XA1967”NAâ”Å
[3]@•s“™Ž®‚ւ̏µ‘ҁA‘åŠÖM—YE‘åŠÖ´‘¾A‹ß‘ã‰ÈŠwŽÐA1987”N
[4]@•s“™Ž®‚̍HŠw‚ւ̉ž—pAŠC’ÃãàAX–ko”ŁA2004”N
[5]@•s“™Ž®iƒ‚ƒmƒOƒ‰ƒt‚SjAõŽæOA‰ÈŠwV‹»VŽÐA1990”N

•s“™Ž®‚Ì–„‘ ’n
[1]@Maths problems@http://www.kalva.demon.co.uk/index.html
[2]@IMOƒŠƒ“ƒNW@http://imo.math.ca/

201 F‚P‚R‚Ql–Ú‚Ì‘f”‚³‚ñF05/03/20 21:30:38
>200
ySierpinski‚Ì•s“™Ž®z
@[>200]‚Ì‚Æ‚«A@‚`^(n-1)¥‚g † ‚f^n † ‚`¥‚g^(n-1).
(—ªØ)
@‚e ß ‚`^(n-1)¥‚g/‚f^n ‚Æ‚¨‚«A‚e†1 ‚ðŽ¦‚·B
@n‚ÉŠÖ‚·‚é‹A”[–@‚É‚æ‚éB
@n=2 ‚Ì‚Æ‚« ‚`‚g=x(1)x(2)=‚f^2 ‚¾‚©‚ç“™†¬—§A‚e=1.
@n‚ɑ΂µ‚Ь‚è—§‚‚Ƃ·‚éBx(n+1)=x ' ‚Æ‚¨‚­‚Æ n+1 ‚ɑ΂µ‚Ä‚Í
@‚`' = (n‚`+ x ')/(n+1), ‚f ' = (‚f^n¥x ')^(1/(n+1)), ‚g ' = ‚g(n+1)x '/(‚g+nx ').
@‚e/‚e ' = {‚`^(n-1)/‚`'^n}(‚g+nx ') = {‚`^(n-1)/‚`'^n}{n‚`' -(n-1)‚` -(‚`-‚g)/(n+1)}
@… {‚`^(n-1)/‚`'^n}{n‚`' -(n-1)‚`} = {nt-(n-1)}/(t^n) … 1, ‚±‚±‚É tß‚`'/‚`. (©š)
@ˆ ‚e '†‚e†c†1.
@x(k) ‚Ì‘ã‚í‚è‚É 1/x(k) ‚ðl‚¦‚ê‚΁A‰E‘¤‚àŽ¦‚¹‚éB(I)
‚Ê‚é‚Û

202 F201F05/03/20 21:37:43
>200 (>201‚Ì•â‘«)@

y•â‘èz‚`†‚g.
@(—ªØ) ‚`^‚g = (1/n^2){ƒ°[i=1,n] x(i)}{ƒ°[j=1,n] 1/x(j)}
@= 1 + (1/n^2)ƒ°[i<j] {x(i)/x(j) +x(j)/x(i) -2}
@= 1 + (1/n^2)ƒ°[i<j] {x(i)-x(j)}^2 /[x(i)x(j)] † 1. (I)

203 F201F05/03/20 22:05:10
>200 (>201‚Ì•â‘«)
yšz@t > -1 Ë t^n † nt -(n-1).
(—ªØ)
(i) t†1‚Ì‚Æ‚«
@t^(n-1) + t^(n-2) + ... + t^2 + t + 1 † n.
@‚Ì—¼•Ó‚É t-1 ‚ð‚©‚¯‚ê‚Î t^n - 1 † nt - n ‚ª“¾‚ç‚ê‚éB
(ii) -1ƒtƒ1‚Ì‚Æ‚«
@1 + t + t^2 + ... + t^(n-2) + t^(n-1) … n.
@‚Ì—¼•Ó‚É 1-t ‚ð‚©‚¯‚ê‚Î 1 - t^n … n - nt ‚ª“¾‚ç‚ê‚éB
‚¢‚¸‚ê‚̏ꍇ‚à t^n † nt-(n-1) ‚ª¬‚è—§‚B@(I)

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¡ ‚±‚̃XƒŒƒbƒh‚͉ߋŽƒƒO‘qŒÉ‚ÉŠi”[‚³‚ê‚Ä‚¢‚Ü‚·

šƒXƒ}ƒz”Łš ŒfŽ¦”Â‚É–ß‚é ‘S•” ‘O100 ŽŸ100 ÅV50

read.cgi ver 05.04.02 2018/11/22 Walang Kapalit š
FOX š DSO(Dynamic Shared Object)