Èô¸÷ÏîΪÕýÊýµÄÊýÁÐ{an£©µÄǰnÏîºÍΪSn£¬Ê×Ïîa1=1£¬a2=3£¬µãP£¨
Sn+1
£¬Sn+2£©£¨n¡ÊN+£©ÔÚº¯Êýy=£¨x+1£©2µÄͼÏóÉÏ
£¨1£©Çóa3£»
£¨2£©ÇóÊýÁÐ{an£©µÄͨÏʽ£»
£¨3£©ÉèÊýÁÐ{cn£©µÄͨÏʽΪcn=
an
an+t
£¬ÊÇ·ñ´æÔÚÕûÊýt£¬Ê¹µÃÊýÁÐ{cn£©ÖдæÔÚÏîck£¨k¡Ý3£¬k¡ÊN+£©£¬Âú×ãc1£¬c2£¬ck£º¹¹³ÉµÈ²îÊýÁУ¬Èô´æÔÚ£¬ÇëÇó³öËùÓзûºÏÌõ¼þµÄtµÄÖµ£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®
¿¼µã£ºÊýÁÐÓë²»µÈʽµÄ×ÛºÏ
רÌ⣺µÈ²îÊýÁÐÓëµÈ±ÈÊýÁÐ
·ÖÎö£º£¨1£©ÓÉÒÑÖªÌõ¼þµÃSn+2=(
Sn+1
+1)2
£¬Áîn=1£¬Ôòa1+a2+a3=(
a1+a2
+1)2
£¬ÓÉ´ËÄÜÇó³öa3£®
£¨2£©ÓÉSn+2=(
Sn+1
+1)2
£¬µÃ
Sn+2
-
Sn+1
=1
£¬´Ó¶øµÃµ½ÊýÁÐ{
Sn
}ÊÇÒÔ
S1
ΪÊ×Ï1Ϊ¹«²îµÄµÈ²îÊýÁУ¬ÓÉ´ËÄÜÇó³öÊýÁÐ{an£©µÄͨÏʽ£®
£¨3£©cn=
2n-1
2n-1+t
£¬ÒªÊ¹c1£¬c2£¬ck³ÉµÈ²îÊýÁУ¬±ØÐë
6
3+t
=
1
1+t
+
2k-1
2k-1+t
£¬ÓÉ´ËÄÜÇó³öËùÓзûºÏÌõ¼þµÄtÖµ£®
½â´ð£º ½â£º£¨1£©¡ßµãP£¨
Sn+1
£¬Sn+2£©£¨n¡ÊN+£©ÔÚº¯Êýy=£¨x+1£©2µÄͼÏóÉÏ£¬
¡àSn+2=(
Sn+1
+1)2
£¬¡­£¨1·Ö£©
Áîn=1£¬ÔòS3=£¨
S2
+1
£©2£¬¡­£¨2·Ö£©
¼´a1+a2+a3=(
a1+a2
+1)2
£¬
¡àa3=(
a1+a2
+1)2-a1-a2
=£¨
1+3
+1)2-1-3=5
2-1-3=5£®¡­£¨3·Ö£©
£¨2£©ÓÉSn+2=(
Sn+1
+1)2
£¬µÃ
Sn+2
-
Sn+1
=1
£®¡­£¨4·Ö£©
ÓÖ
S2
-
S1
=
a1+a2
-
a1
=1
£¬¡­£¨5·Ö£©
¡àÊýÁÐ{
Sn
}ÊÇÒÔ
S1
ΪÊ×Ï1Ϊ¹«²îµÄµÈ²îÊýÁУ¬
¡à
Sn
=
S1
+(n-1)¡Á1
£¬¼´Sn=n2£¬¡­£¨6·Ö£©
µ±n¡Ý2ʱ£¬an=Sn-Sn-1
=n2-£¨n-1£©2
=2n-1£¬¡­£¨8·Ö£©
¡ßa1=1Ò²Âú×ãÉÏʽ£¬
¡àan=2n-1£®¡­£¨9·Ö£©
£¨3£©ÓÉ£¨2£©Öª£¬cn=
an
an+t
=
2n-1
2n-1+t
£¬
Ҫʹc1£¬c2£¬ck³ÉµÈ²îÊýÁУ¬±ØÐë2c2=c1+ck£¬
¼´
6
3+t
=
1
1+t
+
2k-1
2k-1+t
£¬¡­£¨10·Ö£©
»¯¼òµÃk=3+
4
t-1
£®¡­£¨12·Ö£©
¡ßk¡Ý3£¬k¡ÊN*£¬ÇÒtΪÕûÊý£¬¡àt-1Ö»ÄÜΪ1£¬2£¬4£¬¡­£¨13·Ö£©
¡àËùÓзûºÏÌõ¼þµÄtֵΪ2£¬3£¬5£®¡­£¨14·Ö£©
µãÆÀ£º±¾Ì⿼²éÊýÁеÄͨÏʽµÄÇ󷨣¬¿¼²é·ûºÏÌõ¼þµÄʵÊýÖµÊÇ·ñ´æÔÚµÄÅжÏÓëæË·¨£¬½âÌâʱҪÈÏÕæÉóÌ⣬עÒâµÈ²îÊýÁеÄÐÔÖʵÄÁé»îÔËÓã®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªº¯Êýf£¨x£©=sin£¨2¦Øx-
¦Ð
6
£©-
1
2
ͼÏóÏàÁÚÁ½Ìõ¶Ô³ÆÖá¼äµÄ¾àÀëΪ
¦Ð
2
£¬
£¨¢ñ£©Çóº¯Êýf£¨x£©µÄ×îСÕýÖÜÆÚºÍµ¥µ÷ÔöÇø¼ä£»
£¨¢ò£©º¯Êýf£¨x£©Í¼ÏóÏòÓÒÆ½ÒƦգ¨¦Õ£¾0£©¸öµ¥Î»ºó¶ÔÓ¦º¯ÊýΪżº¯Êý£¬Çó¦Õ

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªº¯Êýf£¨x£©=lg£¨1+x£©-lg£¨1-x£©£¬a¡¢b¡Ê£¨-1£¬1£©£¬ÇÒf£¨
a+b
1+ab
£©=1£¬f£¨
a-b
1+ab
£©=2£¬Çóf£¨a£©£¬f£¨b£©µÄÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

½â²»µÈʽ£º3x2-x-4£¾0£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖª
cos¦Á+cos¦Â=-
3
2
a
cos¦Ácos¦Â=
a2-1
4
£¬Çócos¦Á£¬cos¦Â£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

Èçͼ£¬°ë¾¶Îª1µÄÔ²O£¬¡ÏAOB=¡ÏBOC=¡ÏCOA=
2¦Ð
3
£¬µãA0£¬B0£¬C0·Ö±ðÊǰ뾶OA¡¢OB¡¢COÉϵ͝µã£¬ÇÒOA0=OB0=OC0£¬·Ö±ð¹ýA0£¬B0£¬C0×÷°ë¾¶OA¡¢OB¡¢COµÄ´¹Ïߣ¬½»Ô²OÓëA1£¬A2£¬B1£¬B2£¬C1£¬C2£¬¹ýA2£¬B1·Ö±ð×÷OA¡¢OBµÄƽÐÐÏßA2MºÍB1M½»ÓÚµãM£¬¹ýB2£¬C1·Ö±ð×÷OB¡¢OCµÄƽÐÐÏßB2NºÍC1N½»ÓÚµãN£¬¹ýC2£¬A1·Ö±ð×÷OC¡¢OAµÄƽÐÐÏßC2PºÍA1P½»ÓÚµãP£¬ÓÉA1A2MB1B2NC1C2PΧ³ÉͼËùʾµÄÆ½ÃæÇøÓò£¨ÒõÓ°²¿·Ö£©£¬¼ÇËüµÄÃæ»ýΪy£¬Éè¡ÏA2OA=¦È£¬ÓÃy=f£¨¦È£©±íʾy¹ØÓڦȵĺ¯Êý£®
£¨1£©Éè¦È¡Ê£¨0£¬
¦Ð
3
]£¬Çóy=f£¨¦È£©µÄ½âÎöʽ£»
£¨2£©ÔÚ£¨1£©µÄÌõ¼þÏ£¬Çóy=f£¨¦È£©µÄ×î´óÖµ£¬²¢Çó³öµ±º¯ÊýÈ¡×î´óÖµÊÇʱtan2¦ÈµÄÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÊýÁÐ{an}ÖУ¬µã£¨an£¬an+1£©£¨n¡ÊN*£©ÔÚÖ±Ïßx-y+1=0ÉÏ£¬ÇÒa2=2£®
£¨¢ñ£©ÇóÖ¤£ºÊýÁÐ{an}ÊǵȲîÊýÁУ¬²¢Çóan£»
£¨¢ò£©Éèbn=3an£¬ÊýÁÐ{bn}µÄǰnÏîºÍΪSn£¬Èô¶ÔÈÎÒân¡ÊN*£¬¶¼ÓÐ(n+1)(2Sn+3)¡Ü¦Ë•4nºã³ÉÁ¢£¬ÇóʵÊý¦ËµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖª¶¯Ô²¹ýµãM£¨-
3
£¬0£©£¬ÇÒÓëÔ²N£º£¨x-
3
£©2+y2=16ÏàÄÚÇУ®
£¨¢ñ£©Çó¶¯Ô²µÄÔ²ÐÄPµÄ¹ì¼£·½³Ì£»
£¨¢ò£©ÒÑÖªµãA£¨2£¬0£©£¬µãB£¨1£¬0£©£¬¹ýµãBÇÒбÂÊΪk1£¨k1¡Ù0£©µÄÖ±ÏßlÓ루¢ñ£©ÖеĹ켣ÏཻÓÚC¡¢DÁ½µã£¬Ö±ÏßAC¡¢AD·Ö±ð½»Ö±Ïßx=3ÓÚE¡¢FÁ½µã£¬Ïß¶ÎEFµÄÖеãΪQ£®¼ÇÖ±ÏßQBµÄбÂÊΪk2£¬ÇóÖ¤£ºk1•k2Ϊ¶¨Öµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÇúÏßf£¨x£©=x3ÔÚx=n£¨n¡ÊN*£©´¦µÄÇÐÏßÓëxÖáµÄ½»µãºá×ø±êΪan£¬ÔòÊýÁÐ{
1
anan+1
}µÄǰ8ÏîºÍΪ
 
£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸