ÒÑÖªÕýÏîÊýÁÐ{an}µÄÊ×Ïîa1£½£¬º¯Êýf£¨x£©£½£¬g£¨x£©£½£®

   £¨1£©ÈôÕýÏîÊýÁÐ{an}Âú×ãan£«1£½f£¨an£©£¨n¡ÊN*£©£¬Ö¤Ã÷£º{}ÊǵȲîÊýÁУ¬²¢ÇóÊýÁÐ{an}µÄͨÏʽ£»

   £¨2£©ÈôÕýÏîÊýÁÐ{an}Âú×ãan£«1¡Üf£¨an£©£¨n¡ÊN*£©£¬ÊýÁÐ{bn}Âú×ãbn£½£¬Ö¤Ã÷£ºb1£«b2£«¡­£«bn<1£»

   £¨3£©ÈôÕýÏîÊýÁÐ{an}Âú×ãan£«1£½g£¨an£©£¬ÇóÖ¤£º|an£«1£­an|¡Ü¡¤£¨£©n£­1£®

Ö¤Ã÷£º£¨1£©¡ßan£«1£½f£¨an£©£½£¬¡à£½£½£«1£¬¼´£­£½1£¬

¡à{}ÊÇÒÔ2ΪÊ×Ï1Ϊ¹«²îµÄµÈ²îÊýÁУ®

¡à£½2£«£¨n£­1£©£¬¼´an£½£®£¨3·Ö£©

£¨2£©Ö¤Ã÷£º¡ßan£«1¡Ü£¬an>0£¬¡à¡Ý£¬¼´£­¡Ý1£®

µ±n¡Ý2ʱ£¬£­£½£¨£­£©£«£¨£­£©£«¡­£«£¨£­£©¡Ýn£­1£¬

¡à¡Ýn£«1£¬¡àan¡Ü£®

µ±n£½1ʱ£¬ÉÏʽҲ³ÉÁ¢£¬¡àan¡Ü£¨n¡ÊN*£©£¬

¡àbn£½¡Ü<£½£­£¬

¡àb1£«b2£«¡­£«bn<£¨1£­£©£«£¨£­£©£«¡­£«£¨£­£©£½1£­<1£®£¨8·Ö£©

£¨3£©¡ßa1£½£¬a2£½g£¨a1£©£½£¬a2£­a1£½£­£½>0£®

ÓÖ¡ßan£«1£­an£½£­£½£¬

Óɵü´ú¹ØÏµ¿ÉÖª£¬an£«1£­an>0£¬¡àan¡Ýa1£½£®

Ó֡ߣ¨2£«an£©£¨2£«an£­1£©£½£¨2£«£©£¨2£«an£­1£©£½5£«4an£­1¡Ý7£¬

¡à¡Ü£¬

¡à|an£«1£­an|£½|an£­an£­1|¡Ü|an£­an£­1|£¬

¡à|an£«1£­an|¡Ü|an£­an£­1|¡Ü£¨£©2|an£­1£­an£­2|¡Ü¡­

¡Ü£¨£©n£­1|a2£­a1|£½£¨£©n£­1£®£¨13·Ö£©

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÕýÏîÊýÁÐ{an}Âú×㣺a1=3£¬£¨2n-1£©an+2=£¨2n+1£©an-1+8n2£¨n£¾1£¬n¡ÊN*£©
£¨1£©ÇóÖ¤£ºÊýÁÐ{
an
2n+1
}
ΪµÈ²îÊýÁУ¬²¢ÇóÊýÁÐ{an}µÄͨÏîan£®
£¨2£©Éèbn=
1
an
£¬ÇóÊýÁÐ{bn}µÄǰnÏîºÍΪSn£¬²¢ÇóSnµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

¶¨Ò壺³Æ
n
a1+a2+¡­+an
Ϊn¸öÕýÊýa1£¬a2£¬¡­£¬anµÄ¡°¾ùµ¹Êý¡±£¬ÒÑÖªÕýÏîÊýÁÐ{an}µÄǰnÏîµÄ¡°¾ùµ¹Êý¡±Îª
1
2n
£¬Ôò
lim
n¡ú¡Þ
nan
sn
£¨¡¡¡¡£©
A¡¢0
B¡¢1
C¡¢2
D¡¢
1
2

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÕýÏîÊýÁÐanÖУ¬a1=2£¬µã(
an
£¬an+1)
ÔÚº¯Êýy=x2+1µÄͼÏóÉÏ£¬ÊýÁÐbnÖУ¬µã£¨bn£¬Tn£©ÔÚÖ±Ïßy=-
1
2
x+3
ÉÏ£¬ÆäÖÐTnÊÇÊýÁÐbnµÄǰÏîºÍ£®£¨n¡ÊN+£©£®
£¨1£©ÇóÊýÁÐanµÄͨÏʽ£»
£¨2£©ÇóÊýÁÐbnµÄǰnÏîºÍTn£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÕýÏîÊýÁÐ{an}Âú×ãa1=1£¬an+1=an2+2an£¨n¡ÊN+£©£¬Áîbn=log2£¨an+1£©£®
£¨1£©ÇóÖ¤£ºÊýÁÐ{bn}ΪµÈ±ÈÊýÁУ»
£¨2£©¼ÇTnΪÊýÁÐ{
1
log2bn+1log2bn+2
}
µÄǰnÏîºÍ£¬ÊÇ·ñ´æÔÚʵÊýa£¬Ê¹µÃ²»µÈʽTn£¼log0.5(a2-
1
2
a)
¶Ô?n¡ÊN+ºã³ÉÁ¢£¿Èô´æÔÚ£¬Çó³öʵÊýaµÄȡֵ·¶Î§£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÕýÏîÊýÁÐ{an}£¬Sn=
1
8
(an+2)2

£¨1£©ÇóÖ¤£º{an}ÊǵȲîÊýÁУ»
£¨2£©Èôbn=
1
2
an-30
£¬ÇóÊýÁÐ{bn}µÄǰnÏîºÍ£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸