#1
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͹ءÃÁ
$¶éÒ$
$$A = \frac{1}{\frac{1}{2007^2}+\frac{1}{2008^2}+\frac{1}{2009^2}+\ldots +\frac{1}{2548^2}+\frac{1}{2549^2}}$$ $áÅéÇ$ $$\frac{A}{50}$$ $à»ç¹¨Ó¹Ç¹àµçÁ·Õè¹éÍ·ÕèÊØ´à·èÒäÃ$ 18 ÁԶعÒ¹ 2011 06:41 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 6 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ T ♥ Math |
#2
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¾ÔÁ¾ìÍÐäüԴµÃ§ä˹ºéÒ§ÁÑéÂ
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#3
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àËÁ×͹ͧ¤ì»ÃСͺ¢Í§ «Ô¡ÁèÒÂѧäÁè¤ÃºàŹФÃѺ
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#4
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¢Íâ·´¤ÃѺ ¾ÔÁ⨷Âì¼Ô´
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#5
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ÂѧäÁèà¢éÒã¨àŤÃѺ ËÃ×ͨоÔÁ¾ìà»ç¹ n ãËéËÁ´ËÃ×Íà»ÅèÒ
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Vouloir c'est pouvoir |
#6
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à»ÅÕè¹⨷Âìà»ç¹ i ËÃ×Í n ãËéËÁ´ ¨Ò¡¹Ñé¹´ÙµÑÇÍÂèÒ§¨Ò¡Ë¹éÒ¹Õé áéÅéÇÅͧ¹Óä»»ÃÐÂØ¡µìãªé´Ù¤ÃѺ.
http://www.mathcenter.net/sermpra/se...pra18p03.shtml |
#7
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͹ءÃÁ¤ÃѺ
$¶éÒ$
$$A = \frac{1}{\frac{1}{2007^2}+\frac{1}{2008^2}+\frac{1}{2009^2}+\ldots +\frac{1}{2548^2}+\frac{1}{2549^2}}$$ $áÅéÇ \frac{A}{50} à»ç¹¨Ó¹Ç¹àµçÁ·Õè¹éÍ·ÕèÊØ´à·èÒäÃ$ |
#8
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$\dfrac{A}{50}$ äÁèà»ç¹¨Ó¹Ç¹àµçÁ¹Ð
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#9
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⨷Âì¶ÒÁËҨӹǹàµçÁ·Õè¹éÍ·ÕèÊØ´·Õèã¡Åé $\frac{A}{50}$ á¹è¹Í¹ÇèÒ $\frac{A}{50}$ äÁèà»ç¹¨Ó¹Ç¹àµçÁÍÂÙèáÅéǤÃѺ
⨷Âì¢é͹Õéà»ç¹â¨·Âìã¹ Eximus ÊÁѾÕèÊØ¸Õ ¶éÒ¼Á¨ÓäÁè¼Ô´Åͧä»à»Ô´æËÒ´Ù¤ÃѺ à©ÅÂÍÂÙèã¹¹Ñé¹ ¶éÒäÁèÁÕà´ÕëÂǼÁàÍÒÁÒŧãËé
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"ªÑèÇâÁ§Ë¹éÒµéͧ´Õ¡ÇèÒà´ÔÁ!" 21 ÁԶعÒ¹ 2011 01:49 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Keehlzver |
#10
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ãËé $S = \frac{1}{2007^2} + ...+ \frac{1}{2549^2}$ à¹×èͧ¨Ò¡ $\int_{2007}^{2549}\frac{1}{x^2}\,dx < S < \int_{2006}^{2549}\frac{1}{x^2}\,dx$ ´Ñ§¹Ñé¹ $ \frac{542}{(2549)(2007)}<S < \frac{543}{(2549)(2006)}$ ´Ñ§¹Ñé¹ $ \frac{(2549)(2006)}{(543)(50)} < \frac{A}{50} = \frac{1}{50S} <\frac{(2549)(2007)}{(542)(50)}$ $188\frac{9094}{(543)(50)} <\frac{A}{50} < 188\frac{21043}{(542)(50)}$ ¨Ö§ä´éÇèÒ $[\frac{A}{50}] = 188$
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The Lost Emic <<-- ˹ѧÊ×Íà©Å¢éÍÊͺÃдѺ»ÃжÁ¹Ò¹ÒªÒµÔ EMIC ¤ÃÑ駷Õè 1 - ¤ÃÑ駷Õè 8 ªØ´ÊØ´·éÒ ËŧÁÒ 21 ÁԶعÒ¹ 2011 03:09 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ gon |
#11
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$\frac{1}{A}=\dfrac{1}{2007^2} + \dfrac{1}{2008^2} + \dfrac{1}{2009^2} + ... + \dfrac{1}{2549^2}$
$\because \ \ \dfrac{1}{2007^2} > \dfrac{1}{2007 \times 2008} $ áÅÐ $ \dfrac{1}{2008^2} > \dfrac{1}{2008 \times 2009} $ . . . $\dfrac{1}{2549^2} > \dfrac{1}{2549 \times 2550}$ áÅÐ $\dfrac{1}{2007^2} + \dfrac{1}{2008^2} + \dfrac{1}{2009^2} + ... + \dfrac{1}{2549^2} > \dfrac{1}{2007 \times 2008} + \dfrac{1}{2008 \times 2009} + \dfrac{1}{2009 \times 2010} + ... + \dfrac{1}{2549 \times 2550}$ ´Ñ§¹Ñé¹ $\frac{1}{A} > \dfrac{1}{2007 \times 2008} + \dfrac{1}{2008 \times 2009} + \dfrac{1}{2009 \times 2010} + ... + \dfrac{1}{2549 \times 2550}$ $\frac{1}{A} > (\dfrac{1}{2007} - \dfrac{1}{2008} ) + (\dfrac{1}{2008} - \dfrac{1}{2009} ) + (\dfrac{1}{2009} - \dfrac{1}{2010} ) + . . . + (\dfrac{1}{2549} - \dfrac{1}{2550} )$ $\frac{1}{A} > \dfrac{1}{2007} - \dfrac{1}{2550} $ $\frac{1}{A} > \dfrac{543}{2007 \times 2550} $ $A < \dfrac{2007 \times 2550}{543} $ $\frac{A}{50} < \dfrac{2007 \times 2550}{543 \times 50} $ $\frac{A}{50} < 188.5027 $ ´Ñ§¹Ñ鹨ӹǹàµçÁ·ÕèÁÕ¤èÒÁÒ¡·ÕèÊØ´áµèäÁèà¡Ô¹ $\frac{A}{50} $ ¤×Í 188
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ÁÒËÒ¤ÇÒÁÃÙéäÇéµÔÇËÅÒ¹ áµèËÅÒ¹äÁèàÍÒàÅ¢áÅéÇ à¢éÒÁÒ·ÓàÅ¢àÍÒÁѹÍÂèÒ§à´ÕÂÇ ¤ÇÒÁÃÙéà»ç¹ÊÔè§à´ÕÂÇ·ÕèÂÔè§ãËé ÂÔè§ÁÕÁÒ¡ ÃÙéÍÐäÃäÁèÊÙé ÃÙé¨Ñ¡¾Í (¡àÇ鹤ÇÒÁÃÙé äÁèµéͧ¾Í¡çä´é ËÒäÇéÁÒ¡æáËÅдÕ) (áµè¡çÍÂèÒãËéÁÒ¡¨¹·èÇÁËÑÇ àÍÒµÑÇäÁèÃÍ´) |
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