Question

16£®ÊµÑéÓë̽¾¿£º
Èý½ÇµãÕóÇ°nÐеĵãÊý¼ÆËã
ÈçͼÊÇÒ»¸öÈý½ÇµãÕ󣬴ÓÉÏÏòÏÂÊýÓÐÎÞÊý¶àÐУ¬ÆäÖеÚÒ»ÐÐÓÐ1¸öµã£¬µÚ¶þÐÐÓÐ2¸öµã¡­µÚnÐÐÓÐn¸öµã¡­ÈÝÒ×·¢ÏÖ£¬Èý½ÇµãÕóÖÐÇ°4ÐеĵãÊýµÄºÍΪ10£¬ÄãÄÜÇó³öÇ°24ÐеãÊýµÄºÍÊǶàÉÙÂð£¿
ÎÒÃÇÓÃÊÔÑéµÄ·½·¨£¬¼´ÓÉÉ϶øϵØÖðÐеÄÏà¼ÓÆäµãÊý£¬ËäÈ»ÄãÄÜ·¢ÏÖ1+2+3+4+¡­+23+24=300£®¼´Ç°24ÐеĵãÊýºÍÊÇ300£¬µ«ÊÇÕâÑùÑ°ÕÒ´ð°¸ÐèÒª»¨·Ñ½Ï¶àʱ¼ä£¬ÏÂÃæÎÒÃÇÒ»ÆðÀ´Ì½¾¿Óüò±ãµÄ·½·¨µÃ³ö½á¹û£®
ÎÒÃÇÏÈ̽ÇóÈý½ÇµãÕóÖÐÇ°nÐеĵãÊýºÍÓënµÄÊýÁ¿¹Øϵ£ºÇ°nÐеĵãÊýµÄºÍÊÇ1+2+3+¡­+£¨n-2£©+£¨n-1£©+n£¬¿ÉÒÔ·¢ÏÖ£®
2¡Á[1+2+3+¡­+£¨n-2£©+£¨n-1£©+n]=[1+2+3+¡­+£¨n-2£©+£¨n-1£©+n]+[n+£¨n-1£©+£¨n-2£©+¡­3+2+1]°ÑÁ½¸öÖÐÀ¨ºÅÖеĵÚÒ»ÏîÏà¼Ó£¬µÚ¶þÏîÏà¼Ó¡­µÚnÏîÏà¼Ó£¬ÉÏʽµÈºÅµÄºó±ß±äÐÎΪÕân¸öСÀ¨ºÅ¶¼µÈÓÚn+1£¬Õû¸öʽ×ÓµÈÓÚn£¨n+1£©£¬ÓÚÊǵõ½1+2+3+¡­+£¨n-2£©+£¨n-1£©+n=$\frac{1}{2}$n£¨n+1£©Õâ¾ÍÊÇ˵£¬Èý½ÇµãÕóÖÐÇ°nÏîµÄµãÊýµÄºÍÊÇ$\frac{1}{2}$n£¨n+1£©ÓÚÊÇ£¬Ò×µÃÇ°24ÐеãÊýµÄºÍΪ$\frac{1}{2}$¡Á24¡Á£¨24+1£©=300
ÇëÄã¸ù¾ÝÉÏÊö²ÄÁϻشðÏÂÁÐÎÊÌ⣺
£¨1£©Ó¦ÓãºÇóÈý½ÇµãÕóÖÐÇ°100ÐеãÊýµÄºÍ£»
£¨2£©ÍØÕ¹£ºÈç¹û°ÑͼÖеÄÈý½ÇµãÕóÖи÷ÐеãÊýÒÀ´ÎÌæ»»³É2£¬4£¬6£¬¡­£¬2n£¬¡­£¬ÊÔÓú¬nµÄÕûʽ±íʾÈý½ÇµãÕóÖÐÇ°nÐеãÊýµÄºÍ£®

Answer 1

·ÖÎö £¨1£©ÀûÓÃÔĶÁ²ÄÁϸø³öµÄ·½·¨¼ÆËãµÃ³ö´ð°¸¼´¿É£»
£¨2£©ÁÐʽÀûÓÃÌáÈ¡¹«Òòʽ·¨£¬½øÒ»²½ÀûÓøø³öµÄ·½·¨µÃ³ö´ð°¸¼´¿É£®

½â´ð ½â£º£¨1£©1+2+3+4+¡­+100
=$\frac{1}{2}$¡Á100¡Á£¨100+1£©
=5050£»
£¨2£©ÓÉÌâÒâ¿ÉµÃ£º
2+4+6+¡­+2n=2£¨1+2+3+¡­+n£©=2¡Á$\frac{1}{2}$n£¨n+1£©=n£¨n+1£©£®

µãÆÀ ´ËÌ⿼²éͼÐεı仯¹æÂÉ£¬½áºÏͼÐΣ¬ÕÒ³öÊý×ÖµÄÔËËã¹æÂÉ£¬ÀûÓùæÂɽâ¾öÎÊÌ⣮