¶¨Ò壺ÈôÊýÁÐ{An}Âú×ãAn+1=An2£¬Ôò³ÆÊýÁÐ{An}Ϊ¡°Æ½·½µÝÍÆÊýÁС±£®ÒÑÖªÊýÁÐ{an}ÖУ¬a1=2£¬ÇÒan+1=2an2+2an£¬ÆäÖÐnΪÕýÕûÊý£®
£¨1£©Éèbn=2an+1£¬Ö¤Ã÷£ºÊýÁÐ{bn}ÊÇ¡°Æ½·½µÝÍÆÊýÁС±£¬ÇÒÊýÁÐ{lgbn}ΪµÈ±ÈÊýÁУ»
£¨2£©É裨1£©ÖС°Æ½·½µÝÍÆÊýÁС±{bn}µÄÇ°nÏîÖ®»ýΪTn£¬¼´Tn=£¨2a1+1£©£¨2a2+1£©¡­£¨2an+1£©£¬ÇóÊýÁÐ{an}µÄͨÏî¼°Tn¹ØÓÚnµÄ±í´ïʽ£»
£¨3£©¼Çcn=
log
Tn
2an+1
£¬ÇóÊýÁÐ{cn}µÄÇ°nÏîÖ®ºÍSn£¬²¢ÇóʹSn£¾2008µÄnµÄ×îСֵ£®
·ÖÎö£º£¨1£©ÒÀ¾Ý¡°Æ½·½µÝÍÆÊýÁС±¶¨Ò壬½áºÏÌõ¼þan+1=2an2+2an£¬¿ÉÖ¤ÊýÁÐ{bn}ÊÇ¡°Æ½·½µÝÍÆÊýÁС±£¬½ø¶øÓÐlgbn+1=2lgbn£®´Ó¶ø¿ÉÖ¤ÊýÁÐ{lgbn}ΪµÈ±ÈÊýÁУ»
£¨2£©ÓÉ£¨1£©¿ÉµÃan=
1
2
£¨52n-1-1£©£¬¶ÔTn=£¨2a1+1£©£¨2a2+1£©¡­£¨2an+1£©Á½±ßÈ¡¶ÔÊý£¬¿ÉÇóµÃTn=52n-1£®
£¨3£©cn=2-(
1
2
)
n-1
£¬Sn=2n-2+2(
1
2
)
n
£®ÒªÊ¹Sn£¾2008£¬ÔòÓÐn+(
1
2
)
n
£¾1005£¬´Ó¶ø¿ÉÇónµÄ×îСֵ£®
½â´ð£º½â£º£¨1£©ÓÉÌõ¼þan+1=2an2+2an£¬µÃ2an+1+1=4an2+4an+1=£¨2an+1£©2£®
¡à{bn}ÊÇ¡°Æ½·½µÝÍÆÊýÁС±£®¡àlgbn+1=2lgbn£®¡ßlg£¨2a1+1£©=lg5¡Ù0£¬¡à
lg(2an+1+1)
lg(2an+1)
=2£®
¡à{lg£¨2an+1£©}ΪµÈ±ÈÊýÁУ®
£¨2£©¡ßlg£¨2a1+1£©=lg5£¬¡àlg£¨2an+1£©=2n-1?lg5£¬¡à2an+1=52n-1£¬¡àan=
1
2
£¨52n-1-1£©£®
¡ßlgTn=lg£¨2a1+1£©+lg£¨2a2+1£©+¡­+lg£¨2an+1£©=
(1-2n)lg5
1-2
=£¨2n-1£©lg5£®
¡àTn=52n-1£®
£¨3£©cn=
lgTn
lg(2an+1)
=
(2n-1)lg5
2n-1lg5
=
2n-1
2n-1
=2-(
1
2
)
n-1
£¬
¡àSn=2n-[1+
1
2
+(
1
2
)
2
++(
1
2
)
n-1
]=2n-
1-(
1
2
)
n
1-
1
2
=2n-2[1-(
1
2
)
n
]=2n-2+2(
1
2
)
n
£®
ÓÉSn£¾2008µÃ2n-2+2(
1
2
)
n
£¾2008£¬n+(
1
2
)
n
£¾1005£¬
µ±n¡Ü1004ʱ£¬n+(
1
2
)
n
£¼1005£¬µ±n¡Ý1005ʱ£¬n+(
1
2
)
n
£¾1005£¬¡ànµÄ×îСֵΪ1005£®
µãÆÀ£º±¾Ì⿼²éж¨Ò壬½«ÊýÁзŵ½ÐÂÇé¾³ÖУ¬¹Ø¼üÊÇÕýÈ·Àí½âÌâÒ⣬ÍÚ¾òÎÊÌâµÄ±¾ÖÊÓëÒþº¬£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

¶¨Ò壺ÈôÊýÁÐ{An}Âú×ãAn+1=An2£¬Ôò³ÆÊýÁÐ{An}Ϊ¡°Æ½·½ÊýÁС±£®ÒÑÖªÊýÁÐ{an}ÖУ¬a1=2£¬µã£¨an£¬an+1£©ÔÚº¯Êýf£¨x£©=2x2+2xµÄͼÏóÉÏ£¬ÆäÖÐnΪÕýÕûÊý£®
£¨1£©Ö¤Ã÷£ºÊýÁÐ{2an+1}ÊÇ¡°Æ½·½ÊýÁС±£¬ÇÒÊýÁÐ{lg£¨2an+1£©}ΪµÈ±ÈÊýÁУ®
£¨2£©É裨1£©ÖС°Æ½·½ÊýÁС±µÄÇ°nÏîÖ®»ýΪTn£¬¼´Tn=£¨2a1+1£©£¨2a2+1£©¡­£¨2an+1£©£¬ÇóÊýÁÐ{an}µÄͨÏî¼°Tn¹ØÓÚnµÄ±í´ïʽ£®
£¨3£©¼Çbn=log2an+1Tn£¬ÇóÊýÁÐ{bn}µÄÇ°nÏîÖ®ºÍSn£¬²¢ÇóʹSn£¾4020µÄnµÄ×îСֵ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨2012•Ê¯¾°É½Çøһģ£©¶¨Ò壺ÈôÊýÁÐ{An}Âú×ãAn+1=An2£¬Ôò³ÆÊýÁÐ{An}Ϊ¡°Æ½·½µÝÍÆÊýÁС±£®ÒÑÖªÊýÁÐ{an}ÖУ¬a1=2£¬µã£¨an£¬an+1£©ÔÚº¯Êýf£¨x£©=2x2+2xµÄͼÏóÉÏ£¬ÆäÖÐnΪÕýÕûÊý£®
£¨1£©Ö¤Ã÷£ºÊýÁÐ{2an+1}ÊÇ¡°Æ½·½µÝÍÆÊýÁС±£¬ÇÒÊýÁÐ{lg£¨2an+1£©}ΪµÈ±ÈÊýÁУ®
£¨2£©É裨1£©ÖС°Æ½·½µÝÍÆÊýÁС±µÄÇ°nÏîÖ®»ýΪTn£¬¼´Tn=£¨2a1+1£©£¨2a2+1£©¡­£¨2an+1£©£¬ÇóÊýÁÐ{an}µÄͨÏî¼°Tn¹ØÓÚnµÄ±í´ïʽ£®
£¨3£©¼Çbn=log2an+1Tn£¬ÇóÊýÁÐ{bn}µÄÇ°nÏîÖ®ºÍSn£¬²¢ÇóʹSn£¾2011µÄnµÄ×îСֵ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

¶¨Ò壺ÈôÊýÁÐ{an}¶ÔÈÎÒâµÄÕýÕûÊýn£¬¶¼ÓÐ|an+1|+|an|=d£¨dΪ³£Êý£©£¬Ôò³Æ{an}Ϊ¡°¾ø¶ÔºÍÊýÁС±£¬d½Ð×ö¡°¾ø¶Ô¹«ºÍ¡±£¬ÒÑÖª¡°¾ø¶ÔºÍÊýÁС±{an}ÖУ¬a1=2£¬¡°¾ø¶Ô¹«ºÍ¡±d=2£¬ÔòÆäÇ°2012ÏîºÍS2012µÄ×îСֵΪ£¨¡¡¡¡£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

¶¨Ò壺ÈôÊýÁÐ{An}Âú×ãAn+1=
A
2
n
Ôò³ÆÊýÁÐ{An}Ϊ¡°Æ½·½µÝÍÆÊýÁС±£¬ÒÑÖªÊýÁÐ{an}ÖУ¬a1=2£¬µã{an£¬an+1}ÔÚº¯Êýf£¨x£©=2x2+2xµÄͼÏóÉÏ£¬ÆäÖÐnµÄÕýÕûÊý£®
£¨1£©Ö¤Ã÷ÊýÁÐ{2an+1}ÊÇ¡°Æ½·½µÝÍÆÊýÁС±£¬ÇÒÊýÁÐ{lg£¨2an+1£©}ΪµÈ±ÈÊýÁУ»
£¨2£©É裨1£©ÖС°Æ½·½µÝÍÆÊýÁС±µÄÇ°nÏîÖ®»ýΪTn£¬¼´Tn=£¨2a1+1£©£¨2a2+1£©¡­£¨2an+1£©£¬ÇóÊýÁÐ{an}µÄͨÏî¼°Tn¹ØÓÚnµÄ±í´ïʽ£»
£¨3£©¼Çbn=log2an+1Tn£¬ÇóÊýÁÐ{bn}µÄÇ°nÏîºÍSn£¬²¢ÇóʹSn£¾2008µÄnµÄ×îСֵ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨2007•³¤ÄþÇøһģ£©¶¨Ò壺ÈôÊýÁÐ{An}Âú×ãAn+1=An2£¬Ôò³ÆÊýÁÐ{An}Ϊ¡°Æ½·½µÝÍÆÊýÁС±£®ÒÑÖªÊýÁÐ{an}ÖУ¬a1=2£¬µã£¨an£¬an+1£©ÔÚº¯Êýf£¨x£©=x2+4x+2µÄͼÏóÉÏ£¬ÆäÖÐnΪÕýÕûÊý£®
£¨1£©ÅжÏÊýÁÐ{an+2}ÊÇ·ñΪ¡°Æ½·½µÝÍÆÊýÁС±£¿ËµÃ÷ÀíÓÉ£®
£¨2£©Ö¤Ã÷ÊýÁÐ{lg£¨an+2£©}ΪµÈ±ÈÊýÁУ¬²¢ÇóÊýÁÐ{an}µÄͨÏ
£¨3£©ÉèTn=£¨2+a1£©£¨2+a2£©¡­£¨2+an£©£¬ÇóTn¹ØÓÚnµÄ±í´ïʽ£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸