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#1
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⨷Âìã¹ËÑÇ¢éÍ·Äɯպ··ÇÔ¹ÒÁ˹ѧÊ×ÍÊÍǹ
¡Ó˹´$P(x)$à»ç¹¾ËعÒÁ¡ÓÅѧ n ·ÕèÊÍ´¤Åéͧ¡Ñº $P(x)=2^k k\in {1,2,3,4,....,n+1}$ ¨§ËÒ $P(n+2)$
».Å.¼Áµéͧ¡ÒÃá¤èÇÔ¸ÕËÒ $P(0)$ ¤ÃѺà¾ÃÒÐÇÔ¸Õ·Õè¼Á¤Ô´Áѹµéͧãªé P(0) ÍèФÃѺ áµè¶éÒã¤ÃÁÕÇÔ¸ÕÍ×蹡ç¨Ð´ÕÁÒ¡àŹФÃѺ
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math or physic ÊͺÁËÔ´ÅàÊÃ稤èͤԴÅСѹ ºÒ§·Õ¡ç...äÁèÃÙéÊԹР|
#2
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#3
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¶éÒ⨷Âìà»ç¹áººà´ÕÂǡѺ¤Ø³ nooonuii ºÍ¡
Åͧãªé P(x) µÑǹÕé¤ÃѺ $$ P(x)= \bigg( 1+ \binom{x}{1}+\binom{x}{2} +\cdots +\binom{x}{n} \bigg) + \frac{(x-1)(x-2)...(x-n)}{n!} $$ â´Â $ \binom{x}{i}$ à»ç¹¾ËعÒÁ´Õ¡ÃÕ i ¡Ó˹´â´Â $ \binom{x}{i} = \frac{x(x-1)...(x-i+1)}{i!}$
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#4
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§Ñ鹶éÒ $x<n$
$P(x)$ ¡çËÒ¤èÒäÁèä´éËÃ×ͤÃѺ
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#5
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ËÒä´é¤ÃѺ ´Ù·Õè¹ÔÂÒÁ¢Í§ $\binom{x}{i}$ ´Õ¡ÇèÒ¤ÃѺ
Áѹ¡ç¤×;ËعÒÁ¹Õèàͧ ¶éÒâ§ä»ËÒ $\binom{n}{i}$ ¨Ð·ÓãË駧 ·Õè¼Á¤Ô´äÇé¡ç¤ÅéÒÂæ¡Ñ¹¤×ÍÊÃéÒ§ $Q(x)=1+\dfrac{x}{1!}+\dfrac{x(x-1)}{2!}+\cdots+\dfrac{x(x-1)\cdots (x-n+1)}{n!}$ áÅéÇ¡ç¾ÔÊÙ¨¹ìÇèÒ $P(x)=kQ(x)$ ÊÓËÃѺºÒ§ $k$ $k$ ËÒä´é¨Ò¡ $P(n+1)$ ¤ÃѺ
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#6
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#7
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math or physic ÊͺÁËÔ´ÅàÊÃ稤èͤԴÅСѹ ºÒ§·Õ¡ç...äÁèÃÙéÊԹР07 ¾ÄȨԡÒ¹ 2010 17:24 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ nut@satit |
#8
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1. ¹ÔÂÒÁ $f:A\to B$ â´Â $f(S)=S^{c}$
ÊÁÁµÔÇèÒ $S^c=T^c$ ¨Ðä´é $(S^c)^c=(T^c)^c$ $S=T$ ´Ñ§¹Ñé¹ $f$ à»ç¹¿Ñ§¡ìªÑ¹Ë¹Ö觵èÍ˹Öè§ ¶éÒ¡Ó˹´ $T\in B$ ¨Ðä´éÇèÒ $n\not\in T$ ¹Ñ蹤×Í $n\in T^c$ ´Ñ§¹Ñé¹àÅ×Í¡ $S=T^c$ à¹×èͧ¨Ò¡ $n\in S$ ¨Ðä´é $S\in A$ áÅÐä´éÇèÒ $f(S)=S^c=(T^c)^c=T$ ´Ñ§¹Ñé¹ $f$ à»ç¹¿Ñ§¡ìªÑ¹·ÑèǶ֧
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