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#2
16 ÊÔ§ËÒ¤Á 2009, 15:36
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ãËé $ S_m = S_n $
à¹×èͧ¨Ò¡â¨·Âì¡Ó˹´ãËé ÁÕ¾¨¹ìáá áÅмŵèÒ§ÃèÇÁà·èҡѹ ´Ñ§¹Ñé¹ ¡Ó˹´ãËé $a_1$ à»ç¹¾¨¹ì·Õè 1 áÅÐ d á·¹¼ÅµèÒ§ÃèÇÁ $ ¨Ò¡ S_m = S_n $ $ \frac{m}{2}(a_1 + a_m) = \frac{n}{2}(a_1 + a_n) $ $ m(a_1 + a_1 + (m-1)d) = n(a_1 + a_1 + (n-1)d) $ $ m(2a_1 + md - d) = n( 2a_1 + nd - d) $ $ 2ma_1 + m^2d - md = 2na_1 + n^2d - nd $ $ 2ma_1 - 2na_1 + m^2d - n^2d - md + nd =0 $ $ 2a_1(m-n) + d(m+n)(m-n) - d(m-n) = 0 $ $ 2a_1 + d(m+n) - d = 0$ â´Â·Õè $m - n \not= 0$ ä´éÇèÒ $m \not= n $ $ 2a_1 + (m+n-1)d = 0 $ $ \frac{m+n}{2} ( 2a_1 + (m+n-1)d ) = 0 (\frac{m+n}{2}) $ $ S_{m+n} = 0 $ äÁèá¹èã¨ÇèÒÁյçä˹¼Ô´¾ÅÒ´ÃÖ»èÒÇÍèФÃѺ áµè¹èҨлÃÐÁÒ³¹Õé¤ÃѺ 
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16 ÊÔ§ËÒ¤Á 2009 15:39 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 3 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ B º .... 
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