2019°æ¸ß¿¼ÊýѧһÂÖ¸´Ï°µÚ5ÕÂÊýÁÐ5.4ÊýÁÐÇóºÍѧ°¸ÎÄ

n1

(2)ÓÉ(1)µÃ£¬cn£½n£­£¬

2?n£«1??n£«2?

n??1?12

¹ÊTn£½c1£«c2£«¡­£«cn£½?£«£«¡­£«n?£­?2??233?24

£«

1

£«¡­£«334

1?.

??n£«1??n£«2??

12n112n1111nÉèFn£½£«£«¡­£«n£¬ÔòFn£½2£«3£«¡­£«n£«1£¬×÷²îµÃFn£½£«2£«¡­£«n£­n£«1£¬

242222222222ËùÒÔFn£½2£­n£«2

2

n. 11111111111

ÉèGn£½£«£«¡­£«£½£­£«£­£«¡­£«£­£½£­£¬ËùÒÔ

233334?n£«1??n£«2?2334n£«1n£«22n£«21?3n£«2n£«2?11

Tn£½2£­n£­?£­£½£­n£«. ?2n£«2?2n£«2?22

17£®(20172ɽ¶«¸ß¿¼)ÒÑÖª{an}ÊǸ÷Ïî¾ùΪÕýÊýµÄµÈ±ÈÊýÁУ¬ÇÒa1£«a2£½6£¬a1a2£½a3. (1)ÇóÊýÁÐ{an}µÄͨÏʽ£»

(2){bn}Ϊ¸÷Ïî·ÇÁãµÄµÈ²îÊýÁУ¬ÆäÇ°nÏîºÍΪSn.ÒÑÖªS2n£«1£½bnbn£«1£¬ÇóÊýÁÐ??µÄÇ°n?an??bn?

ÏîºÍTn.

½â (1)Éè{an}µÄ¹«±ÈΪq£¬ ÓÉÌâÒâÖªa1(1£«q)£½6£¬a1q£½a1q£¬

ÓÖan>0£¬ÓÉÒÔÉÏÁ½Ê½ÁªÁ¢·½³Ì×é½âµÃa1£½2£¬q£½2£¬ ËùÒÔan£½2. (2)ÓÉÌâÒâÖª

?2n£«1??b1£«b2n£«1?

£½(2n£«1)bn£«1£¬

2

n2

2

S2n£«1£½

ÓÖS2n£«1£½bnbn£«1£¬bn£«1¡Ù0£¬ ËùÒÔbn£½2n£«1. Áîcn£½£¬Ôòcn£½

bnan2n£«1

. n2

Òò´ËTn£½c1£«c2£«¡­£«cn

3572n£­12n£«1£½£«2£«3£«¡­£«n£­1£«n£¬ 2222213572n£­12n£«1ÓÖTn£½2£«3£«4£«¡­£«n£«n£«1£¬ 222222Á½Ê½Ïà¼õµÃ

1?2n£«113?11

Tn£½£«?£«2£«¡­£«n£­1?£­n£«1£¬

2?222?222n£«5

ËùÒÔTn£½5£­n.

2

18£®ÔڵȱÈÊýÁÐ{an}ÖУ¬a1>0£¬n¡ÊN£¬ÇÒa3£­a2£½8£¬ÓÖa1£¬a5µÄµÈ±ÈÖÐÏîΪ16. (1)ÇóÊýÁÐ{an}µÄͨÏʽ£»

*

111

(2)Éèbn£½log4an£¬ÊýÁÐ{bn}µÄÇ°nÏîºÍΪSn£¬ÊÇ·ñ´æÔÚÕýÕûÊýk£¬Ê¹µÃ£«£«£«¡­£«S1S2S3

1

Sn

*

a3£­a2£½8£¬Ôòa2£½8£¬q£½2£¬a1£½4£¬ËùÒÔan£½2n£«1.

(2)bn£½log42

n£«1

£½

n£«1

2

£¬

.

Sn£½b1£«b2£«¡­£«bn£½

1£½n?n£«3?

4

Sn1?44?1

£½?£­?£¬

n?n£«3?3?nn£«3?

1111ËùÒÔ£«£«£«¡­£« S1S2S3Sn11?4?111111

£½?£­£«£­£«£­£«¡­£«£­

nn£«3?3?142536?111?4?11

£­£­£½?1£«£«£­?

3?23n£«1n£«2n£«3?11?4114?1£«£«£½3£­3??

363?n£«1n£«2n£«3?11?224?1£«£«£½£­3??.

93?n£«1n£«2n£«3?122

µ±n£½1ʱ£¬£½1<2<£»

S19

11?22111224?1

£«£«µ±n¡Ý2ʱ£¬£«£«¡­£«£½£­??<<3.

S1S2Sn93?n£«1n£«2n£«3?9¹Ê´æÔÚk£½3ʱ£¬¶ÔÈÎÒâµÄn¡ÊN¶¼ÓÐ 1

*

S1S2S3

111

£«£«£«¡­£«<3.

Sn