ÉèµÈ±ÈÊýÁÐ{an}µÄÇ°nÏîºÍΪSn£¬µÈ²îÊýÁÐbnµÄÇ°nÏîºÍΪTn£¬ÒÑÖªSn=2n+1-c+1£¨ÆäÖÐcΪ³£Êý£©£¬b1=1£¬b2=c£®
£¨1£©Çó³£ÊýcµÄÖµ¼°ÊýÁÐ{an}£¬bnµÄͨÏʽanºÍbn£®
£¨2£©Éèdn=
bn
an
£¬ÉèÊýÁÐdnµÄÇ°nÏîºÍΪDn£¬Èô²»µÈʽm¡ÜDn£¼k¶ÔÓÚÈÎÒâµÄn¡ÊN*ºã³ÉÁ¢£¬ÇóʵÊýmµÄ×î´óÖµÓëÕûÊýkµÄ×îСֵ£®
£¨3£©ÊԱȽÏ
1
T1
+
1
T2
+
1
T3
+¡­+
1
Tn
Óë2µÄ´óС¹Øϵ£¬²¢¸ø³öÖ¤Ã÷£®
·ÖÎö£º£¨1£©ÓÉÌâÉèÖª£¬Sn-1=2n-c+1£¬an=Sn-Sn-1=2n£¨n¡Ý2£©£¬ËùÒÔa1=21=2£»ÁíÒ»·½Ã棬µ±n=1ʱ£¬a1=S1=22-c+1=5-c£¬ËùÒÔc=3£¬
´Ó¶øbn=2n-1£®
£¨2£©ÓÉdn=
2n-1
2n
£¬ÖªDn=d1+d2+d3+d4+¡­+dn-1+dnDn=
1
21
+
3
22
+
5
23
+
7
24
++
2n-3
2n-1
+
2n-1
2n
£¬ÔÙÓôíλÏà¼õ·¨Çó³öDn=3-
2n+3
2n
£®È»ºóÀûÓÃDnÊǵ¥µ÷µÝÔöµÄ£¬ÇóʵÊýmµÄ×î´óÖµºÍÕûÊýkµÄ×îСֵ£®
£¨3£©ÓÉbn=2n-1µÃTn=n2£¬
1
Tn
=
1
n2
£¼
1
n(n-1)
=
1
n-1
-
1
n
£¬ËùÒÔÓÉÁÑÏîÇóºÍ·¨Öª
1
T1
+
1
T2
+
1
T3
++
1
Tn
£¼2£®
½â´ð£º½â£º£¨1£©ÓÉÌâ¿ÉµÃµ±n¡Ý2ʱ£¬Sn-1=2n-c+1
´Ó¶øan=Sn-Sn-1=2n£¨n¡Ý2£©£¬
ÓÖÓÉÓÚ{an}ΪµÈ±ÈÊýÁУ¬ËùÒÔan=2n£¨n¡ÊN*£©£¬
ËùÒÔa1=21=2£»ÁíÒ»·½Ã棬µ±n=1ʱ£¬a1=S1=22-c+1=5-c
ËùÒÔc=3£¬´Ó¶øbn=2n-1

£¨2£©ÓÉ£¨1£©µÃdn=
2n-1
2n

ËùÒÔDn=d1+d2+d3+d4++dn-1+dnDn=
1
21
+
3
22
+
5
23
+
7
24
++
2n-3
2n-1
+
2n-1
2n
¢Ù
´Ó¶ø
1
2
Dn=
1
22
+
3
23
+
5
24
+
7
25
++
2n-3
2n
+
2n-1
2n+1
¢Ú
¢Ù-¢ÚµÃ
1
2
Dn=
1
21
+
2
22
+
2
23
+
2
24
++
2
2n
-
2n-1
2n+1

½âµÃDn=3-
2n+3
2n

ÓÉÓÚDnÊǵ¥µ÷µÝÔöµÄ£¬ÇÒ
2n+3
2n
£¾0
£¬ËùÒÔD1¡ÜDn£¼3£¬¼´
1
2
¡ÜDn£¼3

ËùÒÔʵÊýmµÄ×î´óֵΪ
1
2
£¬ÕûÊýkµÄ×îСֵΪ3£®

£¨3£©ÓÉbn=2n-1¿ÉÇóµÃTn=n2£¬
µ±n¡Ý2ʱ£¬
1
Tn
=
1
n2
£¼
1
n(n-1)
=
1
n-1
-
1
n

ËùÒÔ
1
T1
+
1
T2
+
1
T3
++
1
Tn
=1+(
1
1
-
1
2
)+(
1
2
-
1
3
)+(
1
3
-
1
4
)++(
1
n-1
-
1
n
)
=2-
1
n
£¼2

ËùÒÔ
1
T1
+
1
T2
+
1
T3
++
1
Tn
£¼2
µãÆÀ£º±¾Ì⿼²éÊýÁеÄÐÔÖʺÍÓ¦Ó㬽âÌâʱҪÈÏÕæÉóÌ⣬עÒâÁÑÏîÇóºÍ·¨µÄÔËÓã®
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°¸