ÌâÄ¿ÄÚÈÝ
ÒÑÖªµã£¨n£¬an£©£¨n¡ÊN*£©ÔÚº¯Êýf£¨x£©=-6x-2µÄͼÏóÉÏ£¬ÊýÁÐ{an}µÄÇ°nÏîºÍΪSn£®£¨¢ñ£©ÇóSn£»
£¨¢ò£©Éècn=an+8n+3£¬ÊýÁÐ{dn}Âú×ãd1=c1£¬dn+1=cdn£¨n¡ÊN*£©£®ÇóÊýÁÐ{dn}µÄͨÏʽ£»
£¨¢ó£©Éèg£¨x£©ÊǶ¨ÒåÔÚÕýÕûÊý¼¯Éϵĺ¯Êý£¬¶ÔÓÚÈÎÒâµÄÕýÕûÊýx1¡¢x2£¬ºãÓÐg£¨x1x2£©=x1g£¨x2£©+x2g£¨x1£©³ÉÁ¢£¬ÇÒg£¨2£©=a£¨aΪ³£Êý£¬ÇÒa¡Ù0£©£¬¼Çbn=
g(
| ||
dn+1 |
·ÖÎö£º£¨¢ñ£©ÓÉÌâÒâ¿ÉÖª{an}ÊÇÒÔa1=-8ΪÊ×Ï²îΪ-6µÄµÈ²îÊýÁУ®ÓÉ´Ë¿ÉÒÔÇóµÃSn=-3n2-5n£®
£¨¢ò£©ÓÉcn=an+8n+3=-6n-2+8n+3=2n+1£¨n¡ÊN*£©£¬dn+1=cdn=2dn+1£¬¿ÉÖªdn+1+1=2£¨dn+1£©£¨n¡ÊN*£©£®ÔÙÓÉd1=c1=3£¬¿ÉÖª{dn+1}ÊÇÊ×ÏîΪd1+1=4£¬¹«±ÈΪ2µÄµÈ±ÈÊýÁУ®ÓÉ´ËÄܹ»ÇóµÃdn=2n+1-1£®
£¨¢ó£©½â·¨Ò»£ºÓÉÌâÒâ¿ÉÖªbn+1-bn=
-
=
-
=
£®ÓÉ´Ë¿ÉÖªÊýÁÐ{bn}ÊǵȲîÊýÁУ®
½â·¨¶þ£ºÒòΪg£¨x1x2£©=x1g£¨x2£©+x2g£¨x1£©³ÉÁ¢£¬ÇÒg£¨2£©=a£¬¹Êg(
)=g(2n)=2n-1g(2)+2g(2n-1)=an•2n-1£¬ÓÉ´Ë¿ÉÖªbn+1-bn=
£®Òò´Ë£¬ÊýÁÐ{bn}ÊǵȲîÊýÁУ®
£¨¢ò£©ÓÉcn=an+8n+3=-6n-2+8n+3=2n+1£¨n¡ÊN*£©£¬dn+1=cdn=2dn+1£¬¿ÉÖªdn+1+1=2£¨dn+1£©£¨n¡ÊN*£©£®ÔÙÓÉd1=c1=3£¬¿ÉÖª{dn+1}ÊÇÊ×ÏîΪd1+1=4£¬¹«±ÈΪ2µÄµÈ±ÈÊýÁУ®ÓÉ´ËÄܹ»ÇóµÃdn=2n+1-1£®
£¨¢ó£©½â·¨Ò»£ºÓÉÌâÒâ¿ÉÖªbn+1-bn=
g(2n) |
2n+1 |
g(2n-1) |
2n |
2n-1a+2g(2n-1) |
2n+1 |
g(2n-1) |
2n |
a |
4 |
½â·¨¶þ£ºÒòΪg£¨x1x2£©=x1g£¨x2£©+x2g£¨x1£©³ÉÁ¢£¬ÇÒg£¨2£©=a£¬¹Êg(
dn+1 |
2 |
a |
4 |
½â´ð£º½â£º£¨¢ñ£©ÓÉÒÑÖªan=-6n-2£¬¹Ê{an}ÊÇÒÔa1=-8ΪÊ×Ï²îΪ-6µÄµÈ²îÊýÁУ®
ËùÒÔSn=-3n2-5n£®
£¨¢ò£©ÒòΪcn=an+8n+3=-6n-2+8n+3=2n+1£¨n¡ÊN*£©£¬dn+1=cdn=2dn+1£¬Òò´Ëdn+1+1=2£¨dn+1£©£¨n¡ÊN*£©£®
ÓÉÓÚd1=c1=3£¬
ËùÒÔ{dn+1}ÊÇÊ×ÏîΪd1+1=4£¬¹«±ÈΪ2µÄµÈ±ÈÊýÁУ®
¹Êdn+1=4¡Á2n-1=2n+1£¬ËùÒÔdn=2n+1-1£®
£¨¢ó£©½â·¨Ò»£ºg(
)=g(2n)=2n-1g(2)+2g(2n-1)£¬
Ôòbn=
=
+
£¬bn+1=
+
.bn+1-bn=
-
=
-
=
£®
ÒòΪaΪ³£Êý£¬ÔòÊýÁÐ{bn}ÊǵȲîÊýÁУ®
½â·¨¶þ£ºÒòΪg£¨x1x2£©=x1g£¨x2£©+x2g£¨x1£©³ÉÁ¢£¬ÇÒg£¨2£©=a£¬
¹Êg(
)=g(2n)=2n-1g(2)+2g(2n-1)=2n-1g£¨2£©+2[2n-2g£¨2£©+2g£¨2n-2£©]=2¡Á2n-1g£¨2£©+22g£¨2n-2£©=2¡Á2n-1g£¨2£©+22[2n-3g£¨2£©+2g£¨2n-3£©]=3¡Á2n-1g£¨2£©+23g£¨2n-3£©¨T£¨n-1£©¡Á2n-1g£¨2£©+2n-1g£¨2£©=n•2n-1g£¨2£©=an•2n-1£¬
ËùÒÔbn=
=
=
n£®
Ôòbn+1-bn=
£®
ÓÉÒÑÖªaΪ³£Êý£¬Òò´Ë£¬ÊýÁÐ{bn}ÊǵȲîÊýÁУ®
ËùÒÔSn=-3n2-5n£®
£¨¢ò£©ÒòΪcn=an+8n+3=-6n-2+8n+3=2n+1£¨n¡ÊN*£©£¬dn+1=cdn=2dn+1£¬Òò´Ëdn+1+1=2£¨dn+1£©£¨n¡ÊN*£©£®
ÓÉÓÚd1=c1=3£¬
ËùÒÔ{dn+1}ÊÇÊ×ÏîΪd1+1=4£¬¹«±ÈΪ2µÄµÈ±ÈÊýÁУ®
¹Êdn+1=4¡Á2n-1=2n+1£¬ËùÒÔdn=2n+1-1£®
£¨¢ó£©½â·¨Ò»£ºg(
dn+1 |
2 |
Ôòbn=
2n-1g(2)+2g(2n-1) |
2n+1 |
a |
4 |
g(2n-1) |
2n |
a |
4 |
g(2n) |
2n+1 |
g(2n) |
2n+1 |
g(2n-1) |
2n |
2n-1a+2g(2n-1) |
2n+1 |
g(2n-1) |
2n |
a |
4 |
ÒòΪaΪ³£Êý£¬ÔòÊýÁÐ{bn}ÊǵȲîÊýÁУ®
½â·¨¶þ£ºÒòΪg£¨x1x2£©=x1g£¨x2£©+x2g£¨x1£©³ÉÁ¢£¬ÇÒg£¨2£©=a£¬
¹Êg(
dn+1 |
2 |
ËùÒÔbn=
g(
| ||
dn+1 |
an•2n-1 |
2n+1 |
a |
4 |
Ôòbn+1-bn=
a |
4 |
ÓÉÒÑÖªaΪ³£Êý£¬Òò´Ë£¬ÊýÁÐ{bn}ÊǵȲîÊýÁУ®
µãÆÀ£º±¾Ì⿼²éÊýÁеÄÐÔÖʼ°Æä×ÛºÏÔËÓ㬾ßÓÐÒ»¶¨µÄÄѶȣ¬½âÌâʱÈÏÕæÉóÌ⣬×Ðϸ½â´ð£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿