¶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=n2-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=£¬ÇóÖ¤£ºb1++¡­+£¼£®
¡¾´ð°¸¡¿·ÖÎö£º£¨¢ñ£©¸ù¾ÝÌâÒ⣺¡÷an=an+1-an=£¨n+1£©2-£¨n+1£©-n2+n=5n-4£¬ËùÒÔ¡÷an+1-¡÷an=6£®ÓÉ´ËÄܹ»Ö¤Ã÷{¡÷an}ÊǵȲîÊýÁУ®
£¨¢ò£©ÓÉ¡÷2an-¡÷an+1+an=-2n£¬Öª¡÷an+1-¡÷an-¡÷an+1+an=-2n£¬ËùÒÔ¡÷an-an=2n£®ÓÉ´ËÈëÊÖÄܹ»Çó³öÊýÁÐ{an}µÄͨÏʽ£®
£¨¢ó£©ÓÉan=n•2n-1£¬bn===£¬µ±n¡Ý2£¬n¡ÊN*ʱ£¬==£¨-£©£¬ÓÉ´ËÈëÊÖ£¬Äܹ»Ö¤Ã÷b1++¡­+£¼£®
½â´ð£º½â£º£¨¢ñ£©¸ù¾ÝÌâÒ⣺¡÷an=an+1-an=£¨n+1£©2-£¨n+1£©-n2+n=5n-4 £¨2·Ö£©
¡à¡÷an+1-¡÷an=6£®
¡àÊýÁÐ{Dan}ÊÇÊ×ÏîΪ1£¬¹«²îΪ5µÄµÈ²îÊýÁУ®£¨3·Ö£©
£¨¢ò£©ÓÉ¡÷2an-¡÷an+1+an=-2n£¬¡à¡÷an+1-¡÷an-¡÷an+1+an=-2n£¬⇒¡÷an-an=2n£®£¨5·Ö£©
¶ø¡÷an=an+1-an£¬¡àan+1-2an=2n£¬¡à-=£¬£¨6·Ö£©
¡àÊýÁÐ{}¹¹³ÉÒÔΪÊ×ÏΪ¹«²îµÄµÈ²îÊýÁУ¬
¼´=⇒an=n•2n-1£®£¨7·Ö£©
£¨¢ó£©ÓÉ£¨¢ò£©Öªan=n•2n-1£¬
¡àbn===£¨9·Ö£©
¡àµ±n¡Ý2£¬n¡ÊN*ʱ==£¨-£©£¬
¡àb1++¡­+=1+[£¨-£©+£¨-£©+£¨-£©+¡­+£¨-£©+£¨-£©]
=1+£¨+--£©£¼1+£¨+£©=£®
µ±n=1ʱ£¬b1=1£¼£¬ÏÔÈ»³ÉÁ¢£®
¡àb1++¡­+£¼£®£¨12·Ö£©
µãÆÀ£ºµÚ£¨¢ñ£©Ì⿼²éµÈ²îÊýÁеÄÖ¤Ã÷£¬½âÌâʱҪעÒâµÈ²îÊýÁÐÐÔÖʵĺÏÀíÔËÓ㻵ڣ¨¢ò£©Ì⿼²éÊýÁÐͨÏʽµÄÇó½â·½·¨£¬½âÌâʱҪעÒâ¹¹Ôì·¨µÄºÏÀíÔËÓ㻵ڣ¨¢ó£©Ì⿼²éÊýÁÐÇ°nÏîºÍµÄÖ¤Ã÷£¬½âÌâʱҪעÒâÁÑÏîÇóºÍ·¨µÄºÏÀíÔËÓã®
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*£©£»ÀàËƵģ¬¹æ¶¨{¡÷2an}ΪÊýÁÐ{an}µÄ¶þ½×²î·ÖÊýÁУ¬ÆäÖС÷2an=¡÷an+1-¡÷an£¨n¡ÊN*£©£®
£¨¢ñ£©ÒÑÖªÊýÁÐ{an}µÄͨÏʽan=3n2-5n£¨n¡ÊN*£©£¬ÊÔÖ¤Ã÷{¡÷an}ÊǵȲîÊýÁУ»
£¨¢ò£©ÈôÊýÁÐ{an}µÄÊ×Ïîa1=1£¬ÇÒÂú×ã¡÷2an-¡÷an+1+an=-2n£¨n¡ÊN*£©£¬Áîbn=
an
2n
£¬ÇóÊýÁÐ{bn}µÄͨÏʽ£»
£¨¢ó£©ÔÚ£¨¢ò£©µÄÌõ¼þÏ£¬¼Çcn=
a1(n=1)
2n-1
¡÷an
(n¡Ý2£¬n¡ÊN*
£¬ÇóÖ¤£ºc1+
c2
2
+¡­+
cn
n
£¼
17
12
£®

²é¿´´ð°¸ºÍ½âÎö>>

¿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£º½â´ðÌâ

¶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=Êýѧ¹«Ê½n2-Êýѧ¹«Ê½n£¨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=Êýѧ¹«Ê½£¬ÇóÖ¤£ºb1+Êýѧ¹«Ê½+¡­+Êýѧ¹«Ê½£¼Êýѧ¹«Ê½£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º0117 ÆÚÖÐÌâ ÌâÐÍ£º½â´ðÌâ

¶ÔÓÚÊýÁÐ{an}£¬¹æ¶¨ÊýÁÐ{¡÷an}ΪÊýÁÐ{an}µÄÒ»½×²î·ÖÊýÁУ¬ÆäÖС÷an=an+1-an£¨n¡ÊN*£©£»Ò»°ãµØ£¬¹æ¶¨Îª{an}µÄk½×²î·ÖÊýÁУ¬ÆäÖУ¬ÇÒ¡£
£¨1£©
£¨2£©ÈôÊýÁеÄÊ×ÏÇÒÂú×ã £¬ÇóÊýÁм°µÄͨÏʽ£»
£¨3£©ÔÚ£¨2£©µÄÌõ¼þÏ£¬ÅжÏÊÇ·ñ´æÔÚ×îСֵ£¬Èô´æÔÚÇó³öÆä×îСֵ£¬Èô²»´æÔÚ˵Ã÷ÀíÓÉ¡£

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º2011ÄêËÄ´¨Ê¡Ã¼É½Êи߿¼Êýѧ¶þÄ£ÊÔ¾í£¨ÎÄ¿Æ£©£¨½âÎö°æ£© ÌâÐÍ£º½â´ðÌâ

¶ÔÓÚÊýÁÐ{an}£¬¹æ¶¨{¡÷an}ΪÊýÁÐ{an}µÄÒ»½×²î·ÖÊýÁУ¬ÆäÖС÷an=an+1-an£¨n¡ÊN*£©£»ÀàËƵģ¬¹æ¶¨{¡÷2an}ΪÊýÁÐ{an}µÄ¶þ½×²î·ÖÊýÁУ¬ÆäÖС÷2an=¡÷an+1-¡÷an£¨n¡ÊN*£©£®
£¨¢ñ£©ÒÑÖªÊýÁÐ{an}µÄͨÏʽan=3n2-5n£¨n¡ÊN*£©£¬ÊÔÖ¤Ã÷{¡÷an}ÊǵȲîÊýÁУ»
£¨¢ò£©ÈôÊýÁÐ{an}µÄÊ×Ïîa1=1£¬ÇÒÂú×ã¡÷2an-¡÷an+1+an=-2n£¨n¡ÊN*£©£¬Áîbn=£¬ÇóÊýÁÐ{bn}µÄͨÏʽ£»
£¨¢ó£©ÔÚ£¨¢ò£©µÄÌõ¼þÏ£¬¼Çcn=£¬ÇóÖ¤£ºc1++¡­+£¼£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸