1£®ÔÚ¼ÆËã¡°1¡Á2+2¡Á3+¡­+n£¨n+1£©¡±Ê±£¬Ä³Í¬Ñ§Ñ§µ½ÁËÈçÏÂÒ»ÖÖ·½·¨£º
ÏȸÄдµÚkÏk£¨k+1£©=$\frac{1}{3}$[k£¨k+1£©£¨k+2£©-£¨k-1£©k£¨k+1£©]£¬
Óɴ˵Ã1¡Á2=$\frac{1}{3}$£¨1¡Á2¡Á3-0¡Á1¡Á2£©£¬
2¡Á3=$\frac{1}{3}$£¨2¡Á3¡Á4-1¡Á2¡Á3£©£¬
¡­£¬
n£¨n+1£©=$\frac{1}{3}$[n£¨n+1£©£¨n+2£©-£¨n-1£©n£¨n+1£©]
Ïà¼Ó£¬µÃ1¡Á2+2¡Á3+¡­+n£¨n+1£©=$\frac{1}{3}$n£¨n+1£©£¨n+2£©£®
Àà±ÈÉÏÊö·½·¨£¬ÇëÄã¼ÆËã¡°1¡Á2¡Á3¡Á4+2¡Á3¡Á4¡Á+¡­+n£¨n+1£©£¨n+2£©£¨n+3£©¡±£¬Æä½á¹ûÊÇ$\frac{1}{5}n£¨n+1£©£¨n+2£©£¨n+3£©£¨n+4£©$£®£¨½á¹ûд³ö¹ØÓÚnµÄÒ»´ÎÒòʽµÄ»ýµÄÐÎʽ£©

·ÖÎö ±¾Ì⿼²éµÄ֪ʶµãÊÇÀà±ÈÍÆÀí£¬ÊÇÒª¸ù¾ÝÒÑÖªÖиø³öµÄÔÚ¼ÆËã¡°1¡Á2+2¡Á3+¡­+n£¨n+1£©¡±Ê±»¯¼ò˼·£¬¶Ô1¡Á2¡Á3¡Á4+2¡Á3¡Á4¡Á+¡­+n£¨n+1£©£¨n+2£©£¨n+3£©¡±£¬£©µÄ¼ÆËã½á¹û½øÐл¯¼ò£¬´¦ÀíµÄ·½·¨¾ÍÊÇÀà±È£¬½«n£¨n+1£©£¨n+2£©£¨n+3£©½øÐкÏÀíµÄ·Ö½â£®

½â´ð ½â£º¡ßn£¨n+1£©£¨n+2£©£¨n+3£©=$\frac{1}{5}$[n£¨n+1£©£¨n+2£©£¨n+3£©£¨n+4£©-£¨n-1£©n£¨n+1£©£¨n+2£©£¨n+3]
¡à1¡Á2¡Á3¡Á4=$\frac{1}{5}$£¨1¡Á2¡Á3¡Á4¡Á5-0¡Á1¡Á2¡Á3¡Á4£©
2¡Á3¡Á4¡Á5=$\frac{1}{5}$£¨2¡Á3¡Á4¡Á5¡Á6-1¡Á2¡Á3¡Á4¡Á5£©
¡­
n£¨n+1£©£¨n+2£©£¨n+3£©=$\frac{1}{5}$[n£¨n+1£©£¨n+2£©£¨n+3£©£¨n+4£©-£¨n-1£©n£¨n+1£©£¨n+2£©£¨n+3£©]
¡à1¡Á2¡Á3¡Á4+2¡Á3¡Á4¡Á5+¡­+n£¨n+1£©£¨n+2£©£¨n+3£©=$\frac{1}{5}$[£¨1¡Á2¡Á3¡Á4¡Á5-0¡Á1¡Á2¡Á3¡Á4£©+£¨2¡Á3¡Á4¡Á5¡Á6-1¡Á2¡Á3¡Á4¡Á5£©+¡­+n£¨n+1£©£¨n+2£©£¨n+3£©£¨n+4£©-£¨n-1£©n£¨n+1£©£¨n+2£©£¨n+3£©]=$\frac{1}{5}n£¨n+1£©£¨n+2£©£¨n+3£©£¨n+4£©$£®
¹Ê´ð°¸Îª£º$\frac{1}{5}n£¨n+1£©£¨n+2£©£¨n+3£©£¨n+4£©$£®

µãÆÀ Àà±ÈÍÆÀíµÄÒ»°ã²½ÖèÊÇ£º£¨1£©ÕÒ³öÁ½ÀàÊÂÎïÖ®¼äµÄÏàËÆÐÔ»òÒ»ÖÂÐÔ£»£¨2£©ÓÃÒ»ÀàÊÂÎïµÄÐÔÖÊÈ¥ÍÆ²âÁíÒ»ÀàÊÂÎïµÄÐÔÖÊ£¬µÃ³öÒ»¸öÃ÷È·µÄÃüÌ⣨²ÂÏ룩£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

11£®¸´Êý$\frac{2-i}{1+i}$µÄģΪ$\frac{\sqrt{10}}{2}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

12£®ÃüÌâp£º²»µÈʽ|x|+|x+1|£¾mµÄ½â¼¯ÎªR£¬ÃüÌâq£ºº¯Êýf£¨x£©=x2-2mx+1ÔÚ£¨2£¬+¡Þ£©ÉÏÊÇÔöº¯Êý£¬Èôp¡ÅqÎªÕæ£¬p¡ÄqΪ¼Ù£¬ÇóʵÊýmµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

9£®ÔÚδÀ´3ÌìÖУ¬Ä³ÆøÏǫ́Ԥ±¨ÌìÆøµÄ׼ȷÂÊΪ0.8£¬ÔòÔÚδÀ´3ÌìÖУ¬ÖÁÉÙÁ¬Ðø2ÌìÔ¤±¨×¼È·µÄ¸ÅÂÊÊÇ0.768£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

16£®¼×¡¢ÒÒÁ½ÈËÉä»÷£¬»÷ÖаÐ×ӵĸÅÂÊ·Ö±ðΪ0.9£¬0.8£¬ÈôÁ½ÈËͬʱÉä»÷£¬ÔòËûÃǶ¼ÍѰеĸÅÂÊΪ0.02£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

6£®ÔÚ¡÷ABCÖУ¬ÒÑÖªÏòÁ¿$\overrightarrow{AB}$=£¨2£¬2£©£¬|$\overrightarrow{AC}$|=2£¬$\overrightarrow{AB}$•$\overrightarrow{AC}$=-4£¬Ôò¡ÏA=£¨¡¡¡¡£©
A£®$\frac{5¦Ð}{6}$B£®$\frac{¦Ð}{4}$C£®$\frac{2¦Ð}{3}$D£®$\frac{3¦Ð}{4}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

13£®¡°Ë«ÇúÏßCµÄ½¥½üÏßΪy=¡À$\sqrt{2}$x¡±ÊÇ¡°Ë«ÇúÏßCµÄÀëÐÄÂÊΪ$\sqrt{3}$¡±µÄ£¨¡¡¡¡£©
A£®³ä·Ö²»±ØÒªÌõ¼þB£®±ØÒª²»³ä·ÖÌõ¼þ
C£®³äÒªÌõ¼þD£®¼È²»³ä·ÖÒ²²»±ØÒªÌõ¼þ

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

10£®Èôx£¬yÂú×ãÔ¼ÊøÌõ¼þ$\left\{\begin{array}{l}{|x-y|¡Ü2}\\{x+3y-14¡Ü0}\\{x£¬y¡Ê{N}^{*}}\end{array}\right.$£¬Ôòz=x+yµÄ×î´óֵΪ8£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

11£®×÷³öº¯Êýy=|x2-2x-1|Óëy=x2-2|x|-1µÄͼÏ󣬲¢Ð´³öÆäÖµÓò£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸