ÉèµÈ±ÈÊýÁÐ{an}µÄÇ°nÏîºÍΪSn£¬ÒÑÖªan+1=2Sn+2(n¡ÊN*)£®
£¨1£©ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨2£©ÔÚanÓëan+1(n¡ÊN*)Ö®¼ä²åÈën¸ö1£¬¹¹³ÉÈçϵÄÐÂÊýÁУºa1£¬1£¬a2£¬1£¬1£¬a3£¬1£¬1£¬1£¬a4£¬¡­£¬ÇóÕâ¸öÊýÁеÄÇ°2012ÏîµÄºÍ£»
£¨3£©ÔÚanÓëan+1Ö®¼ä²åÈën¸öÊý£¬Ê¹Õân+2¸öÊý×é³É¹«²îΪdnµÄµÈ²îÊýÁУ¨È磺ÔÚa1Óëa2Ö®¼ä²åÈë1¸öÊý¹¹³ÉµÚÒ»¸öµÈ²îÊýÁУ¬Æ乫²îΪd1£»ÔÚa2Óëa3Ö®¼ä²åÈë2¸öÊý¹¹³ÉµÚ¶þ¸öµÈ²îÊýÁУ¬Æ乫²îΪd2£¬¡­ÒÔ´ËÀàÍÆ£©£¬ÉèµÚn¸öµÈ²îÊýÁеĺÍÊÇAn£®ÊÇ·ñ´æÔÚÒ»¸ö¹ØÓÚnµÄ¶àÏîʽg£¨n£©£¬Ê¹µÃAn=g£¨n£©dn¶ÔÈÎÒân¡ÊN*ºã³ÉÁ¢£¿Èô´æÔÚ£¬Çó³öÕâ¸ö¶àÏîʽ£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®
£¨1£©Éèan=a1qn-1£¬
ÓÉan+1=2Sn+2£¬Öª
a1q=2a1+2
a1q2=2(a1+a1q)+2
£¬
½âµÃ
a1=2
q=3
£¬
¹Êan=2¡Á3n-1¡­£¨6·Ö£©
£¨2£©ÒÀÌâÒ⣬µ½anΪֹ£¬ÐµÄÊýÁй²ÓÐ1+2+3+¡­+n=
n(n+1)
2
Ï
Áî
n(n+1)
2
=2012£¬
µÃn=
-1+
1+4024¡Á4
2
¡Ö62.9£¬
¼´µ½a62Ϊֹ£¬ÐµÄÊýÁй²ÓÐ1+2+3+4+¡­+62=
62(62+1)
2
=1953Ï
¹Ê¸ÃÊýÁеÄÇ°2012ÏîµÄºÍΪ£º
a1+a2+¡­+a62+1+2+3+¡­+61+=
2¡Á(1-362)
1-3
+1950
=362+1949£®
£¨3£©ÒÀÌâÒ⣬dn=
2¡Á3n-2¡Á3n-1
n+1
=
4¡Á3n-1
n+1
£¬
An=
(2¡Á3n+2¡Á3n-1)(n+2)
2

=4£¨n+2£©¡Á3n-1£¬
ҪʹAn=g£¨n£©dn£¬
Ôò4£¨n+2£©¡Á3n-1=g£¨n£©¡Á
4¡Á3n-1
n+1
£¬
¡àg£¨n£©=£¨n+2£©¡Á£¨n+1£©=n2+3n+2£¬
¼´´æÔÚg£¨n£©=n2+3n+2Âú×ãÌõ¼þ£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÉèµÈ±ÈÊýÁÐ{an}µÄÇ°nÏîºÍΪSn£¬Èô8a2+a5=0£¬ÔòÏÂÁÐʽ×ÓÖÐÊýÖµ²»ÄÜÈ·¶¨µÄÊÇ£¨¡¡¡¡£©
A¡¢
a5
a3
B¡¢
S5
S3
C¡¢
an+1
an
D¡¢
Sn+1
Sn

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

12¡¢ÉèµÈ±ÈÊýÁÐ{an}µÄÇ°nÏîºÍΪSn£¬ËÈÖªS10=¡Ò03£¨1+2x£©dx£¬S20=18£¬ÔòS30=
21
£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÉèµÈ±ÈÊýÁÐ{an}µÄÇ°nÏîºÍΪSn£¬ÈôS6£ºS3=3£¬ÔòS9£ºS6=
 
£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÉèµÈ±ÈÊýÁÐ{an}µÄÇ°nÏîºÍΪSn£¬Èô
S6
S3
=3£¬Ôò
S9
S6
=£¨¡¡¡¡£©
A¡¢
1
2
B¡¢
7
3
C¡¢
8
3
D¡¢1

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÉèµÈ±ÈÊýÁÐ{an}µÄÇ°n ÏîºÍΪSn£¬Èô
S6
S3
=3£¬Ôò
S9
S3
=
7
7
£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸