1£®ÈôÊýÁÐ{an}Âú×ã¡°¶ÔÈÎÒâÕýÕûÊýn£¬$\frac{{{a_n}+{a_{n+2}}}}{2}¡Ü{a_{n+1}}$ºã³ÉÁ¢¡±£¬Ôò³ÆÊýÁÐ{an}Ϊ¡°²î·ÇÔöÊýÁС±£®
¸ø³öÏÂÁÐÊýÁÐ{an}£¬n¡ÊN*£º
¢Ùan=2n+$\frac{1}{n}$+1£¬¢Úan=n2+1£¬¢Ûan=2n+1£¬¢Üan=ln$\frac{n}{n+1}$£¬¢Ýan=2n+$\frac{1}{n}$£®
ÆäÖÐÊÇ¡°²î·ÇÔöÊýÁС±µÄÓТۢܣ¨Ð´³öËùÓÐÂú×ãÌõ¼þµÄÊýÁеÄÐòºÅ£©£®

·ÖÎö °Ñ$\frac{{{a_n}+{a_{n+2}}}}{2}¡Ü{a_{n+1}}$ºã³ÉÁ¢»¯Îªan+an+2¡Ü2an+1ºã³ÉÁ¢£¬È»ºóÖðÒ»ÑéÖ¤5¸öÊýÁеô𰸣®

½â´ð ½â£º¢ÙÈôan=2n+$\frac{1}{n}$+1Ϊ¡°²î·ÇÔöÊýÁС±£¬Ôò${2}^{n}+\frac{1}{n}+1+{2}^{n+2}+\frac{1}{n+2}+1¡Ü2£¨{2}^{n+1}+\frac{1}{n+1}+1£©$ºã³ÉÁ¢£¬
¼´${2}^{n}¡Ü\frac{-2}{n£¨n+1£©£¨n+2£©}$ºã³ÉÁ¢£¬´ËʽÏÔÈ»²»ÕýÈ·£¬¢Ù²»ÊÇ¡°²î·ÇÔöÊýÁС±£»
¢ÚÈôan=n2+1Ϊ¡°²î·ÇÔöÊýÁС±£¬Ôòn2+1+£¨n+2£©2+1¡Ü2£¨n+1£©2+2£¬
¼´2¡Ü0ºã³ÉÁ¢£¬´ËʽÏÔÈ»²»ÕýÈ·£¬¢Ú²»ÊÇ¡°²î·ÇÔöÊýÁС±£»
¢ÛÈôan=2n+1Ϊ¡°²î·ÇÔöÊýÁС±£¬Ôò2n+1+2£¨n+2£©+1¡Ü2[2£¨n+1£©+1]£¬
¼´0¡Ü0ºã³ÉÁ¢£¬´ËʽÏÔÈ»ÕýÈ·£¬¢ÛÊÇ¡°²î·ÇÔöÊýÁС±£»
¢ÜÈôan=ln$\frac{n}{n+1}$Ϊ¡°²î·ÇÔöÊýÁС±£¬Ôòln$\frac{n}{n+1}$+ln$\frac{n+2}{n+3}$¡Ü2ln$\frac{n+1}{n+2}$£¬
¼´$\frac{n}{n+1}•\frac{n+2}{n+3}¡Ü£¨\frac{n+1}{n+2}£©^{2}$ºã³ÉÁ¢£¬Ò²¾ÍÊÇ2n+3¡Ý0ºã³ÉÁ¢£¬´ËʽÏÔÈ»ÕýÈ·£¬¢ÜÊÇ¡°²î·ÇÔöÊýÁС±£»
¢ÝÈôan=2n+$\frac{1}{n}$Ϊ¡°²î·ÇÔöÊýÁС±£¬Ôò$£¨2n+\frac{1}{n}£©+[2£¨n+2£©+\frac{1}{n+2}]$$¡Ü2[2£¨n+1£©+\frac{1}{n+1}]$£¬
¼´2¡Ü0ºã³ÉÁ¢£¬´ËʽÏÔÈ»²»ÕýÈ·£¬¢Ú²»ÊÇ¡°²î·ÇÔöÊýÁС±£®
¹Ê´ð°¸Îª£º¢Û¢Ü£®

µãÆÀ ±¾ÌâÊÇж¨ÒåÌ⣬¿¼²éÁËÊýÁеĺ¯ÊýÌØÐÔ£¬¿¼²éÁ˼ÆËãÄÜÁ¦£¬ÊÇÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

19£®ÉèËæ»ú±äÁ¿X£ºB£¨6£¬$\frac{1}{3}$£©£¬ÔòD£¨X£©µÈÓÚ£¨¡¡¡¡£©
A£®2B£®$\frac{4}{3}$C£®$\frac{2}{3}$D£®$\frac{8}{3}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

12£®ÈçͼËÄÀâ×¶P-ABCDµÄµ×ÃæABCDÊÇÁâÐΣ¬PA¡Íµ×ÃæABCD£¬E£¬F·Ö±ðÊÇAC£¬PBµÄÖе㣬PA=AB=2£¬¡ÏBAD=120¡ã£®
£¨1£©Ö¤Ã÷£ºEF¡ÎÆ½ÃæPCD£»
£¨2£©ÇóEFÓëÆ½ÃæPACËù³É½ÇµÄÕýÏÒÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

9£®É躯Êýf£¨x£©Âú×ãf£¨x£©=f£¨4-x£©£¨x¡ÊR£©£¬ÇÒµ±x£¾2ʱf£¨x£©ÎªÔöº¯Êý£¬¼Ça=f£¨1.10.5£©£¬b=f£¨0.51.1£©£¬c=f£¨log0.5$\frac{1}{16}$£©£¬Ôòa¡¢b¡¢cµÄ´óС¹ØÏµÎª£¨¡¡¡¡£©
A£®c£¼b£¼aB£®c£¼a£¼bC£®b£¼a£¬cD£®a£¼b£¼c

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

16£®Èôx¡¢yÂú×ã$\left\{\begin{array}{l}{2x+5y¡Ý10}\\{2x-3y¡Ü-6}\\{2x+y¡Ü10}\end{array}\right.$£¬Ôòz=x2+y2µÄ×îСֵΪ4£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

6£®ÒÑÖªµãF£¨-c£¬0£©£¨c£¾0£©ÊÇË«ÇúÏß$\frac{x^2}{a^2}-\frac{y^2}{b^2}$=1£¨a£¾0£¬b£¾0£©µÄ×󽹵㣬¹ýFÇÒÆ½ÐÐÓÚË«ÇúÏß½¥½üÏßµÄÖ±ÏßÓëÔ²x2+y2=c2½»ÓÚÁíÒ»µãP£¬ÇÒµãPÔÚÅ×ÎïÏßy2=4cxÉÏ£¬Ôò¸ÃË«ÇúÏßµÄÀëÐÄÂÊµÄÆ½·½ÊÇ$\frac{\sqrt{5}+1}{2}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

13£®Èçͼ£¬ÒÑÖªÍÖÔ²$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄÀëÐÄÂÊΪ$\frac{\sqrt{3}}{2}$£¬ÇÒ¹ýµã£¨$\sqrt{3}$£¬$\frac{1}{2}$£©£®
£¨¢ñ£©Çó¸ÃÍÖÔ²µÄ·½³Ì£»
£¨¢ò£©ÈôA£¬B£¬CΪÍÖÔ²ÉϵÄÈýµã£¨A£¬B²»ÔÚ×ø±êÖáÉÏ£©£¬Âú×ã$\overrightarrow{OC}$=$\frac{3}{5}\overrightarrow{OA}$+$\frac{4}{5}\overrightarrow{OB}$£¬Ö±ÏßOA£¬OB·Ö±ð½»Ö±Ïßl£ºx=3ÓÚM£¬NÁ½µã£¬ÉèÖ±ÏßOA£¬OBµÄбÂÊΪk1£¬k2£®Ö¤Ã÷£ºk1•k2Ϊ¶¨Öµ£¬²¢ÇóÏß¶ÎMN³¤¶ÈµÄ×îСֵ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

10£®Èçͼ£¬ÒÑÖª¶¨µãA£¨1£¬0£©£¬µãBÊǶ¨Ö±Ïßl£ºx=-1Éϵ͝µã£¬¡ÏBOAµÄ½Çƽ·ÖÏß½»ABÓÚC£®
£¨1£©ÇóµãCµÄ¹ì¼£·½³Ì£»
£¨2£©ÈôE£¨-2£¬0£©£¬F£¨2£¬0£©£¬G£¨-1£¬$\frac{1}{2}$£©£¬£¨1£©Öй켣ÉÏÊÇ·ñ´æÔÚÒ»µãQ£¬Ö±ÏßEQ£¬FQÓëyÖá½»µã·Ö±ðΪM£¬N£¬Ê¹µÃ¡ÏMGNÊÇÖ±½Ç£¿Èç¹û´æÔÚ£¬ÇóµãQ×ø±ê£»Èç¹û²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

11£®ÒÑÖª£¨x+1£©n=a0+a1£¨x-1£©+a2£¨x-1£©2+a3£¨x-1£©3+¡­+an£¨x-1£©n£¬£¨ÆäÖÐn¡ÊN*£©
£¨1£©Çóa0¼°${S_n}=\sum_{i=1}^n{a_i}$£»
£¨2£©ÊԱȽÏSnÓ루n-2£©3n+2n2µÄ´óС£¬²¢ËµÃ÷ÀíÓÉ£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸