1£®ÒÑÖªÊýÁÐ{an}µÄǰnÏîºÍSn=-an-${£¨\frac{1}{2}£©}^{n-1}$+2£¨n¡ÊN*£©£®ÊýÁÐ{bn}Âú×ãbn=2nan£®
£¨1£©ÇóÖ¤ÊýÁÐ{bn}ÊǵȲîÊýÁУ¬²¢ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨2£©Éècn=log2$\frac{n}{{a}_{n}}$£¬ÊýÁÐ{$\frac{1}{{c}_{n}{c}_{n+1}}$}µÄǰnÏîºÍΪTn£®Èô²»µÈʽ¦Ë¡ÜTn¶ÔÈÎÓúµÄn¡ÊN*ºã³ÉÁ¢£¬ÇóʵÊý¦ËµÄ×î´óÖµ£®

·ÖÎö £¨1£©ÓÉÊýÁÐ{an}µÄǰnÏîºÍSn=-an-${£¨\frac{1}{2}£©}^{n-1}$+2£¨n¡ÊN*£©£®¿ÉµÃ£ºa1=S1=-a1-1+2£¬½âµÃa1£®µ±n¡Ý2ʱ£¬an=Sn-Sn-1£¬»¯Îª£ºan=$\frac{1}{2}{a}_{{n}_{-1}}$+$£¨\frac{1}{2}£©^{n}$£®Ö»ÒªÖ¤Ã÷£ºbn+1-bn=³£Êý¼´¿É£®
£¨2£©cn=log2$\frac{n}{{a}_{n}}$=n£¬¿ÉµÃ£º$\frac{1}{{c}_{n}{c}_{n+1}}$=$\frac{1}{n£¨n+1£©}$=$\frac{1}{n}-\frac{1}{n+1}$£®ÀûÓá°ÁÑÏîÇóºÍ¡±ÓëÊýÁеĵ¥µ÷ÐÔ¼´¿ÉµÃ³ö£®

½â´ð £¨1£©Ö¤Ã÷£º¡ßÊýÁÐ{an}µÄǰnÏîºÍSn=-an-${£¨\frac{1}{2}£©}^{n-1}$+2£¨n¡ÊN*£©£®
¡àa1=S1=-a1-1+2£¬½âµÃa1=$\frac{1}{2}$£®
µ±n¡Ý2ʱ£¬an=Sn-Sn-1=-an-${£¨\frac{1}{2}£©}^{n-1}$+2-$[-{a}_{n-1}-£¨\frac{1}{2}£©^{n-2}+2]$£¬
»¯Îª£ºan=$\frac{1}{2}{a}_{{n}_{-1}}$+$£¨\frac{1}{2}£©^{n}$£®
¡àbn+1-bn=2n+1an+1-2nan=${2}^{n+1}[\frac{1}{2}{a}_{n}+£¨\frac{1}{2}£©^{n+1}]$-2nan=1£¬
¡àÊýÁÐ{bn}ÊǵȲîÊýÁУ¬Ê×Ïîb1=2a1=1£¬¹«²îΪ1£®
¡àbn=1+£¨n-1£©=n£®
¡àan=$\frac{n}{{2}^{n}}$£®
£¨2£©½â£ºcn=log2$\frac{n}{{a}_{n}}$=n£¬
¡à$\frac{1}{{c}_{n}{c}_{n+1}}$=$\frac{1}{n£¨n+1£©}$=$\frac{1}{n}-\frac{1}{n+1}$£®
¡àÊýÁÐ{$\frac{1}{{c}_{n}{c}_{n+1}}$}µÄǰnÏîºÍΪTn=$£¨1-\frac{1}{2}£©+£¨\frac{1}{2}-\frac{1}{3}£©$+¡­+$£¨\frac{1}{n}-\frac{1}{n+1}£©$=1-$\frac{1}{n+1}$=$\frac{n}{n+1}$£®
²»µÈʽ¦Ë¡ÜTn»¯Îª£º¦Ë¡Ü1-$\frac{1}{n+1}$£¬
¡ß²»µÈʽ¦Ë¡ÜTn¶ÔÈÎÒâµÄn¡ÊN*ºã³ÉÁ¢£¬
¡à$¦Ë¡Ü\frac{1}{2}$£®
¡àʵÊý¦ËµÄ×î´óÖµÊÇ$\frac{1}{2}$£®

µãÆÀ ±¾Ì⿼²éÁ˵ȲîÊýÁеÄͨÏʽ¡¢¡°ÁÑÏîÇóºÍ¡±·½·¨¡¢ÊýÁеĵ¥µ÷ÐÔÓë²»µÈʽµÄÐÔÖÊ¡¢¶ÔÊýµÄÔËËãÐÔÖÊ£¬¿¼²éÁËÍÆÀíÄÜÁ¦Óë¼ÆËãÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

11£®a£¬b±íʾ²»Í¬µÄÖ±Ïߣ¬¦Á£¬¦Â£¬¦Ã±íʾ²»Í¬µÄÆ½Ãæ£®
¢ÙÈô¦Á¡É¦Â=a£¬b?¦Á£¬a¡Íb£¬Ôò¦Á¡Í¦Â£»
¢ÚÈôa?¦Á£¬a´¹Ö±ÓÚ¦ÂÄÚÈÎÒâÒ»ÌõÖ±Ïߣ¬Ôò¦Á¡Í¦Â£»
¢ÛÈô¦Á¡Í¦Â£¬¦Á¡É¦Â=a£¬¦Á¡É¦Ã=b£¬Ôòa¡Íb£»
¢ÜÈôa²»´¹Ö±Æ½Ãæ¦Á£¬Ôòa²»¿ÉÄÜ´¹Ö±ÓÚÆ½Ãæ¦ÁÄÚµÄÎÞÊýÌõÖ±Ïߣ»
¢ÝÈôa¡Í¦Á£¬b¡Í¦Â£¬a¡Îb£¬Ôò¦Á¡Î¦Â£®
ÉÏÊöÎå¸öÃüÌâÖУ¬ÕýÈ·ÃüÌâµÄÐòºÅÊÇ£¨¡¡¡¡£©
A£®¢Ù¢Ú¢ÛB£®¢Ú¢Ü¢ÝC£®¢Ü¢ÝD£®¢Ú¢Ý

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

12£®ÒÑÖªÏòÁ¿$\overrightarrow m=£¨cos\frac{x}{3}£¬\sqrt{3}cos\frac{x}{3}£©$£¬$\overrightarrow n=£¨sin\frac{x}{3}£¬cos\frac{x}{3}£©$£¬$f£¨x£©=\overrightarrow m•\overrightarrow n$£®
 £¨¢ñ£©Çóº¯Êýf£¨x£©µÄµ¥µ÷Çø¼ä£»
£¨¢ò£©Èç¹ûÏȽ«f£¨x£©µÄͼÏóÏò×óÆ½ÒÆ¦Õ£¨¦Õ£¾0£©¸öµ¥Î»£¬ÔÙ±£³Ö×Ý×ø±ê²»±ä£¬ºá×ø±ê±äΪԭÀ´µÄ$\frac{1}{3}$±¶£¬µÃµ½º¯Êýg£¨x£©µÄͼÏó£¬Èôg£¨x£©ÎªÅ¼º¯Êý£¬Çó¦ÕµÄ×îСֵ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

9£®ÔÚÆ½ÃæÖ±½Ç×ø±êϵÖУ¬Ë«ÇúÏßC¹ýµãP£¨1£¬1£©£¬ÇÒÆäÁ½Ìõ½¥½üÏߵķ½³Ì·Ö±ðΪ2x+y=0ºÍ2x-y=0£¬ÔòË«ÇúÏßCµÄ±ê×¼·½³ÌΪ£¨¡¡¡¡£©
A£®$\frac{x^2}{3}-\frac{{4{y^2}}}{3}=1$B£®$\frac{{4{x^2}}}{3}-\frac{y^2}{3}=1$
C£®$\frac{{4{x^2}}}{3}-\frac{y^2}{3}=1$»ò$\frac{x^2}{3}-\frac{{4{y^2}}}{3}=1$D£®$\frac{{4{y^2}}}{3}-\frac{x^2}{3}=1$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

16£®Éè¹ØÓÚxµÄ·½³Ìx2+4mx+4n=0£®
£¨¢ñ£©Èôm¡Ê{1£¬2£¬3}£¬n¡Ê{0£¬1£¬2}£¬Çó·½³ÌÓÐʵ¸ùµÄ¸ÅÂÊ£»
£¨¢ò£©Èôm¡¢n¡Ê{-2£¬-1£¬1£¬2}£¬Çóµ±·½³ÌÓÐʵ¸ùʱ£¬Á½¸ùÒìºÅµÄ¸ÅÂÊ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

6£®ÒÑÖªº¯Êý$f£¨x£©=\left\{\begin{array}{l}x£¬|x|¡Ü1\\ sin\frac{¦Ð}{2}x£¬|x|£¾1\end{array}\right.$ÔòÏÂÁнáÂÛÕýÈ·µÄÊÇ£¨¡¡¡¡£©
A£®º¯Êýf£¨x£©ÔÚ$[-\frac{¦Ð}{2}£¬\frac{¦Ð}{2}]$Éϵ¥µ÷µÝÔöB£®º¯Êýf£¨x£©µÄÖµÓòÊÇ[-1£¬1]
C£®?x0¡ÊR£¬f£¨-x0£©¡Ù-f£¨x0£©D£®?x¡ÊR£¬f£¨-x£©¡Ùf£¨x£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

13£®ÒÑÖªÍÖÔ²µÄÒ»¸ö½¹µãΪF£¨-$\sqrt{3}$£¬0£©£¬ÆäÀëÐÄÂÊΪ$\frac{\sqrt{3}}{2}$£®
£¨1£©Çó¸ÃÍÖÔ²µÄ±ê×¼·½³Ì£»
£¨2£©Ô²x2+y2=$\frac{4}{5}$µÄÈÎÒ»ÌõÇÐÏßÓë¸ÃÍÖÔ²¾ùÓÐÁ½¸ö½»µãA¡¢B£¬ÇóÖ¤0A¡Í0B£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

10£®ÒÑÖª¡÷ABCÖУ¬A=45¡ã£¬B=60¡ã£¬$b=\sqrt{3}$£¬ÄÇôa=$\sqrt{2}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

11£®ÒÑÖªÊýÁÐ{an}Âú×ãa1=1£¬an+1•an=2n£®
£¨1£©Çóan£®
£¨2£©Çó{an}µÄǰnÏîºÍSn£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸