2£®ÒÑÖªÊýÁÐ{an}µÄÇ°nÏîºÍSnÂú×㣺2Sn=3an+n-2£®
£¨1£©ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨2£©Éèbn=log3£¨2an+1-1£©£¬TnΪÊýÁÐ{bn}µÄÇ°nÏîºÍ£¬ÁîMn=$\frac{1}{{T}_{1}}$+$\frac{1}{{T}_{2}}$+¡­+$\frac{1}{{T}_{n}}$ÊÇ·ñ´æÔÚ×î´óµÄÕýÕûÊým£¬Ê¹Mn¡Ý$\frac{m}{4}$¶¼³ÉÁ¢£¿Èô´æÔÚ£¬Çó³ömµÄÖµ£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®

·ÖÎö £¨1£©ÀûÓõÝÍƹØϵ¿ÉµÃ£º${a}_{n}-\frac{1}{2}$=3$£¨{a}_{n-1}-\frac{1}{2}£©$£¬ÔÙÀûÓõȱÈÊýÁеÄͨÏʽ¼´¿ÉµÃ³ö£®
£¨2£©bn=n£¬ÊýÁÐ{bn}µÄÇ°nÏîºÍTn=$\frac{n£¨n+1£©}{2}$£¬¿ÉµÃ$\frac{1}{{T}_{n}}$=2$£¨\frac{1}{n}-\frac{1}{n+1}£©$£®ÀûÓá°ÁÑÏîÇóºÍ¡±¿ÉµÃMn£¬ÔÙÀûÓÃÊýÁеĵ¥µ÷ÐÔ¼´¿ÉµÃ³ö£®

½â´ð ½â£º£¨1£©¡ß2Sn=3an+n-2£¬¡àµ±n=1ʱ£¬2a1=3a1+1-2£¬½âµÃa1=1£®
µ±n¡Ý2ʱ£¬2Sn-1=3an-1+n-3£¬¡à2an=3an-3an-1+1£¬»¯Îª£º${a}_{n}-\frac{1}{2}$=3$£¨{a}_{n-1}-\frac{1}{2}£©$£¬
¡àÊýÁÐ$\{{a}_{n}-\frac{1}{2}\}$ÊǵȱÈÊýÁУ¬Ê×ÏîΪ$\frac{1}{2}$£¬¹«±ÈΪ3£®
¡àan-$\frac{1}{2}$=$\frac{1}{2}¡Á{3}^{n-1}$£¬
¡àan=$\frac{1}{2}$+$\frac{1}{2}¡Á{3}^{n-1}$£®
£¨2£©bn=log3£¨2an+1-1£©=n£¬
ÊýÁÐ{bn}µÄÇ°nÏîºÍTn=$\frac{n£¨n+1£©}{2}$£¬
$\frac{1}{{T}_{n}}$=2$£¨\frac{1}{n}-\frac{1}{n+1}£©$£®
ÁîMn=$\frac{1}{{T}_{1}}$+$\frac{1}{{T}_{2}}$+¡­+$\frac{1}{{T}_{n}}$=2$[£¨1-\frac{1}{2}£©$+$£¨\frac{1}{2}-\frac{1}{3}£©$+¡­+$£¨\frac{1}{n}-\frac{1}{n+1}£©]$=2$£¨1-\frac{1}{n+1}£©$=$\frac{2n}{n+1}$£®
¼ÙÉè´æÔÚ×î´óµÄÕýÕûÊým£¬Ê¹Mn¡Ý$\frac{m}{4}$¶¼³ÉÁ¢£®
Ôòm¡Ü$\frac{8n}{n+1}$£¬
$\frac{8n}{n+1}$=$\frac{8}{1+\frac{1}{n}}$¡Ý4£¬µ±n=1ʱȡµÈºÅ£¬
¡àm¡Ü4£®
¡à´æÔÚ×î´óµÄÕýÕûÊým=4£¬Âú×ãÌõ¼þ£®

µãÆÀ ±¾Ì⿼²éÁ˵ȱÈÊýÁеÄͨÏʽ¡¢¡°ÁÑÏîÇóºÍ¡±¡¢ÊýÁеĵ¥µ÷ÐÔ£¬¿¼²éÁËÍÆÀíÄÜÁ¦Óë¼ÆËãÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

12£®ÒÑÖªÖ±Ïßl¹ýµãP£¨0£¬-2£©£¬ÇÒÓëÒÔA£¨1£¬-1£©B£¨2£¬-4£©Îª¶ËµãµÄÏ߶ÎAB×ÜÓй«¹²µã£¬ÇóÖ±ÏßlÇãб½ÇµÄÈ¡Öµ·¶Î§[0£¬$\frac{¦Ð}{4}$]¡È[$\frac{3¦Ð}{4}$£¬¦Ð£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

13£®ÔÚÕýËÄÀâ׶P-ABCDÖУ¬PA=2£¬EΪPCµÄÖе㣬ÈôÒìÃæÖ±ÏßPAÓëBEËù³É½ÇΪ45¡ã£¬ÔòËÄÀâ׶P-ABCDµÄ¸ßΪ£¨¡¡¡¡£©
A£®$\frac{\sqrt{3}}{3}$B£®$\frac{2\sqrt{3}}{3}$C£®$\sqrt{3}$D£®2$\sqrt{3}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

10£®ÒÑÖªº¯Êýf£¨x£©=2x-$\frac{a}{x}$£¨a£¾0£©£®
£¨1£©ÅжϺ¯Êýf£¨x£©µÄÆæżÐÔ²¢Ö¤Ã÷ÄãµÄ½áÂÛ£»
£¨2£©ÇóÖ¤£ºº¯Êýf£¨x£©ÔÚÇø¼ä£¨0£¬+¡Þ£©ÉÏÊÇÔöº¯Êý£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

17£®ÒÑÖªÊýÁÐ{an}µÄ¸÷ÏÊÇÕýÊý£¬ÆäÇ°nÏîºÍSn=$\frac{{{a}_{n}}^{2}+{a}_{n}}{2}$£¨n¡ÊN*£©£¬ÊýÁÐ{bn}Âú×ãbn=$\frac{121}{n+1}$£¨n¡ÊN*£©£¬Ôòµ±an+bnÈ¡×îСֵʱn=10£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

7£®ÒÑÖªº¯Êýf£¨x£©=b+logax£¨a£¾0ÇÒa¡Ù1£©µÄͼÏó¹ýµã£¨27£¬-1£©£¬Æä·´º¯ÊýµÄͼÏó¹ýµã£¨1£¬3£©£¬Ôòf£¨x£©ÔÚ[9£¬81]ÉϵÄ×î´óֵΪ£¨¡¡¡¡£©
A£®-1B£®0C£®1D£®3

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

14£®ÉèF2£¨c£¬0£©£¨c£¾0£©ÊÇË«ÇúÏߧ¤£º$\frac{{x}^{2}}{{a}^{2}}$-$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾0£¬b£¾0£©µÄÓÒ½¹µã£¬MÊÇË«ÇúÏß×øÖ§Éϵĵ㣬Ï߶ÎMF2ÓëÔ²x2+y2-$\frac{2c}{3}$x+$\frac{{a}^{2}}{9}$=0ÏàÇÐÓëµãD£¬ÇÒ$\overrightarrow{M{F}_{2}}$+3$\overrightarrow{{F}_{2}D}$=$\overrightarrow{0}$£¬ÔòË«ÇúÏߧ¤µÄ½¥½üÏß·½³ÌΪ£¨¡¡¡¡£©
A£®y=$¡À\sqrt{2}$xB£®y=¡À2xC£®y=$¡À\frac{3}{2}$xD£®y=¡À4x

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

11£®ÒÑÖªÔÚƽÃæÖ±½Ç×ø±êϵÖУ¬$\left\{\begin{array}{l}{x¡Ü2}\\{x+y¡Ý4}\\{x-y¡Ý-2}\end{array}\right.$£¬±íʾµÄƽÃæÇøÓòΪ¦¸£¬O£¨0£¬0£©£¬A£¨1£¬0£©£¬ÈôM¡Ê¦¸£®Ôò$\frac{\overrightarrow{OA}•\overrightarrow{OM}}{|\overrightarrow{OM}|}$µÄÈ¡Öµ·¶Î§ÊÇ[-$\frac{\sqrt{10}}{10}$£¬$\frac{\sqrt{2}}{2}$]£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

12£®ÉèPÊǺ¯Êýy=elnxÉÏÒ»µã£¬QÊÇÖ±Ïßy=x+3ÉÏÒ»µã£¬ÔòPQµÄ×îСֵΪ$\frac{3\sqrt{2}}{2}$£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸