¶ÔÓÚÊýÁÐ{an} £¨n=1£¬2£¬¡­£¬m£©£¬ÁîbkΪa1£¬a2£¬¡­£¬akÖеÄ×î´óÖµ£¬³ÆÊýÁÐ{bn}Ϊ{an}µÄ¡°´´ÐÂÊýÁС±£®ÀýÈçÊýÁÐ2£¬1£¬3£¬7£¬5µÄ´´ÐÂÊýÁÐΪ2£¬2£¬3£¬7£¬7£®¶¨ÒåÊýÁÐ{Cn}£ºc1£¬c2£¬c3£¬¡­£¬cmÊÇ×ÔÈ»Êý1£¬2£¬3£¬¡­£¬m£¨m£¾3£©µÄÒ»¸öÅÅÁУ®
£¨¢ñ£©µ±m=5ʱ£¬Ð´³ö´´ÐÂÊýÁÐΪ3£¬4£¬4£¬5£¬5µÄËùÓÐÊýÁÐ{Cn}£»
£¨¢ò£©ÊÇ·ñ´æÔÚÊýÁÐ{Cn}£¬Ê¹ËüµÄ´´ÐÂÊýÁÐΪµÈ²îÊýÁУ¿Èô´æÔÚ£¬Çó³öËùÓеÄÊýÁÐ{Cn}£¬Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®
¡¾´ð°¸¡¿·ÖÎö£º£¨¢ñ£©ÓÉÌâÒâ¿ÉµÃ£¬´´ÐÂÊýÁÐΪ3£¬4£¬4£¬5£¬5µÄËùÓÐÊýÁÐ {Cn}ÓÐÁ½¸ö£®
£¨¢ò£©´æÔÚÊýÁÐ{Cn}£¬Ê¹ËüµÄ´´ÐÂÊýÁÐΪµÈ²îÊýÁУ®ÉèÊýÁÐ{Cn} µÄ´´ÐÂÊýÁÐΪ{ en}£¬Èô{ en}ΪµÈ²îÊýÁУ¬ÉèÆ乫²îΪd£¬¾­¹ý¼ìÑ飬µ±d=0»ò1ʱ£¬´æÔÚÊýÁÐ{Cn}£¬Ê¹ËüµÄ´´ÐÂÊýÁÐΪµÈ²îÊýÁУ®
½â´ð£º½â£º£¨¢ñ£©ÓÉÌâÒâ¿ÉµÃ£¬´´ÐÂÊýÁÐΪ3£¬4£¬4£¬5£¬5µÄËùÓÐÊýÁÐ {Cn}ÓÐÁ½¸ö£¬¼´ÊýÁÐ3£¬4£¬1£¬5£¬2£»
»òÊýÁÐ3£¬4£¬2£¬5£¬1£®  ¡­£¨4·Ö£©
£¨¢ò£©´æÔÚÊýÁÐ{Cn}£¬Ê¹ËüµÄ´´ÐÂÊýÁÐΪµÈ²îÊýÁУ®
ÉèÊýÁÐ{Cn} µÄ´´ÐÂÊýÁÐΪ{ en}£¬£¨n=1£¬2£¬3£¬4¡­£¬m£©£¬
ÒòΪem ÊÇ c1£¬c2£¬c3£¬¡­£¬cm ÖеÄ×î´óÖµ£¬ËùÒÔ em=m£®
ÓÉÌâÒâÖª£¬ekΪ c1£¬c2£¬c3£¬¡­ck ÖÐ×î´óÖµ£¬ËùÒÔ£¬ek¡Üek+1£¬ÇÒ ek¡Ê{1£¬2£¬3£¬¡­£¬m}£®
Èô{ en}ΪµÈ²îÊýÁУ¬ÉèÆ乫²îΪd£¬Ôòd=ek+1-ek¡Ý0 ÇÒd¡ÊN£®
µ±d=0 ʱ£¬{ en}Ϊ³£ÊýÁУ¬ÓÖ em=m£¬ËùÒÔÊýÁÐ{ en}Ϊ m£¬m£¬¡­£¬m£®
´ËʱÊýÁÐ{Cn}ÊÇÊ×ÏîΪmµÄÈÎÒâÒ»¸ö·ûºÏÌõ¼þµÄÊýÁУ®  ¡­£¨8·Ö£©
µ±d=1ʱ£¬ÒòΪem=m£¬ËùÒÔÊýÁÐ{ en} Ϊ1£¬2£¬¡­£¬m£®
´Ëʱ£¬ÊýÁÐ{cn} Ϊ1£¬2£¬3£¬¡­£¬m£®  ¡­£¨10·Ö£©
µ±d¡Ý2ʱ£¬ÒòΪ em=e1+£¨m-1£©d¡Ýe1+£¨m-1£©2=2m-2+e1£¬
ÓÖm£¾3£¬e1 ÎªÕýÕûÊý£¬ËùÒÔ em£¾m£¬ÕâÓë em=m ì¶Ü£¬ËùÒÔ´Ëʱ{ en}²»´æÔÚ£¬¼´²»´æÔÚ{Cn}ʹµÃËüµÄ´´ÐÂÊýÁÐΪ¹«²îd¡Ý2µÄµÈ²îÊýÁУ®¡­£¨13·Ö£©
×ÛÉÏ£¬µ±ÊýÁÐ{Cn}ΪÒÔmΪÊ×ÏîµÄÈÎÒâÒ»¸ö·ûºÏÌõ¼þµÄÊýÁУ¬»ò{Cn}ΪÊýÁÐ1£¬2£¬3£¬¡­£¬mʱ£¬ËüµÄ´´ÐÂÊýÁÐΪµÈ²îÊýÁУ®¡­£¨14·Ö£©
µãÆÀ£º±¾ÌâÖ÷Òª¿¼²é´´ÐÂÊýÁеĶ¨Ò壬µÈ²îÊýÁеĶ¨ÒåºÍÐÔÖÊ£¬ÌåÏÖÁË·ÖÀàÌÖÂÛµÄÊýѧ˼Ï룬ÊôÓÚÖеµÌ⣮
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

¶ÔÓÚÊýÁÐ{an}£¬¹æ¶¨{¡÷an}ΪÊýÁÐ{an}µÄÒ»½×²î·ÖÊýÁУ¬ÆäÖС÷an=an+1-an£¨n¡ÊN*£©£»Ò»°ãµØ£¬¹æ¶¨{¡÷kan}ΪÊýÁÐ{an}µÄk½×²î·ÖÊýÁУ¬ÆäÖС÷kan=¡÷k-1an+1-¡÷k-1an£¬ÇÒk¡ÊN*£¬k¡Ý2£®
£¨¢ñ£©ÒÑÖªÊýÁÐ{an}µÄͨÏʽan=
5
2
n2-
13
2
n£¨n¡ÊN*£©£¬ÊÔÖ¤Ã÷{¡÷an}ÊǵȲîÊýÁУ»
£¨¢ò£©ÈôÊýÁÐ{an}µÄÊ×Ïîa1=1£¬ÇÒÂú×ã¡÷2an-an+1+an=-2n£¨n¡ÊN*£©£¬ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨¢ó£©ÔÚ£¨¢ò£©µÄÌõ¼þÏ£¬¼Çbn=
a1(n=1)
2n-1
¡÷an
(n¡Ý2£¬n¡ÊN*)
£¬ÇóÖ¤£ºb1+
b2
2
+¡­+
bn
n
£¼
17
12
£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

8¡¢¶ÔÓÚÊýÁÐ{an}£¬Èô´æÔÚ³£ÊýM£¬Ê¹µÃ¶ÔÈÎÒân¡ÊN*£¬anÓëan+1ÖÐÖÁÉÙÓÐÒ»¸ö²»Ð¡ÓÚM£¬Ôò¼Ç×÷{an}?M£¬ÄÇôÏÂÁÐÃüÌâÕýÈ·µÄÊÇ£¨¡¡¡¡£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

¶ÔÓÚÊýÁÐ{an}£¬¶¨ÒåÊýÁÐ{bm}ÈçÏ£º¶ÔÓÚÕýÕûÊým£¬bmÊÇʹµÃ²»µÈʽan¡Ým³ÉÁ¢µÄËùÓÐnÖеÄ×îСֵ£®
£¨¢ñ£©Éè{an}Êǵ¥µ÷µÝÔöÊýÁУ¬Èôa3=4£¬Ôòb4=
 
£»
£¨¢ò£©ÈôÊýÁÐ{an}µÄͨÏʽΪan=2n-1£¬n¡ÊN*£¬ÔòÊýÁÐ{bm}µÄͨÏîÊÇ
 
£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨2008•ÉϺ£Ò»Ä££©¹Û²ìÊýÁУº
¢Ù1£¬-1£¬1£¬-1£¬¡­£»
¢ÚÕýÕûÊýÒÀ´Î±»4³ýËùµÃÓàÊý¹¹³ÉµÄÊýÁÐ1£¬2£¬3£¬0£¬1£¬2£¬3£¬0£¬¡­£»
¢Ûan=tan
n¦Ð
3
£¬n=1£¬2£¬3£¬¡­
£¨1£©¶ÔÒÔÉÏÕâЩÊýÁÐËù¹²ÓеÄÖÜÆÚÌØÕ÷£¬ÇëÄãÀà±ÈÖÜÆÚº¯ÊýµÄ¶¨Ò壬ΪÕâÀàÊýÁÐÏÂÒ»¸öÖÜÆÚÊýÁеĶ¨Ò壺¶ÔÓÚÊýÁÐ{an}£¬Èç¹û
´æÔÚÕýÕûÊýT
´æÔÚÕýÕûÊýT
£¬¶ÔÓÚÒ»ÇÐÕýÕûÊýn¶¼Âú×ã
an+T=an
an+T=an
³ÉÁ¢£¬Ôò³ÆÊýÁÐ{an}ÊÇÒÔTΪÖÜÆÚµÄÖÜÆÚÊýÁУ»
£¨2£©ÈôÊýÁÐ{an}Âú×ãan+2=an+1-an£¬n¡ÊN*£¬SnΪ{an}µÄÇ°nÏîºÍ£¬ÇÒS2=2008£¬S3=2010£¬Ö¤Ã÷{an}ΪÖÜÆÚÊýÁУ¬²¢ÇóS2008£»
£¨3£©ÈôÊýÁÐ{an}µÄÊ×Ïîa1=p£¬p¡Ê[0£¬
1
2
£©£¬ÇÒan+1=2an£¨1-an£©£¬n¡ÊN*£¬ÅжÏÊýÁÐ{an}ÊÇ·ñΪÖÜÆÚÊýÁУ¬²¢Ö¤Ã÷ÄãµÄ½áÂÛ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨2012•Í¨ÖÝÇøһģ£©¶ÔÓÚÊýÁÐ{an}£¬´ÓµÚ¶þÏîÆð£¬Ã¿Ò»ÏîÓëËüÇ°Ò»ÏîµÄ²îÒÀ´Î×é³ÉµÈ±ÈÊýÁУ¬³Æ¸ÃµÈ±ÈÊýÁÐΪÊýÁÐ{an}µÄ¡°²îµÈ±ÈÊýÁС±£¬¼ÇΪÊýÁÐ{bn}£®ÉèÊýÁÐ{bn}µÄÊ×Ïîb1=2£¬¹«±ÈΪq£¨qΪ³£Êý£©£®
£¨I£©Èôq=2£¬Ð´³öÒ»¸öÊýÁÐ{an}µÄÇ°4Ï
£¨II£©£¨¢¡£©ÅжÏÊýÁÐ{an}ÊÇ·ñΪµÈ²îÊýÁУ¬²¢ËµÃ÷ÄãµÄÀíÓÉ£»
£¨¢¢£©a1ÓëqÂú×ãʲôÌõ¼þ£¬ÊýÁÐ{an}ÊǵȱÈÊýÁУ¬²¢Ö¤Ã÷ÄãµÄ½áÂÛ£»
£¨III£©Èôa1=1£¬1£¼q£¼2£¬ÊýÁÐ{an+cn}Êǹ«²îΪqµÄµÈ²îÊýÁУ¨n¡ÊN*£©£¬ÇÒc1=q£¬ÇóʹµÃcn£¼0³ÉÁ¢µÄnµÄÈ¡Öµ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸