10£®ÒÑÖªÊýÁÐ{an}µÄǰnÏîºÍSnºÍͨÏîanÂú×ã${S_n}=\frac{1}{2}£¨1-{a_n}£©$£®
£¨1£©ÇóÊýÁÐ{an}µÄͨÏʽ²¢Ö¤Ã÷${S_n}£¼\frac{1}{2}$£»
£¨2£©É躯Êý$f£¨x£©={log_{\frac{1}{3}}}x$£¬bn=f£¨a1£©+f£¨a2£©+¡­+f£¨an£©£¬Èô${T_n}=\frac{1}{b_1}+\frac{1}{b_2}+\frac{1}{b_3}+¡­+\frac{1}{b_n}$£®ÇóTn£®

·ÖÎö £¨1£©Óɵ±n¡Ý2ʱ£¬Sn-1=$\frac{1}{2}$£¨1-an-1£©£¬an=Sn-Sn-1£¬ÕûÀíµÃ£º2an=-an+an-1£¬$\frac{a_n}{{{a_{n-1}}}}=\frac{1}{3}$£¬µ±n=1ʱ£¬${a_1}=\frac{1}{3}$£¬ÊýÁÐ{an}ÊÇÊ×Ïî${a_1}=\frac{1}{3}$£¬¹«±ÈΪ$\frac{1}{3}$µÄµÈ±ÈÊýÁУ¬¼´¿ÉÇóµÃ${a_n}=\frac{1}{3}¡Á{£¨\frac{1}{3}£©^{n-1}}={£¨\frac{1}{3}£©^n}$£¬ÓɵȱÈÊýÁÐǰnÏîºÍ¹«Ê½¿ÉÖª£º${S_n}=\frac{{\frac{1}{3}[{1-{{£¨\frac{1}{3}£©}^n}}]}}{{1-\frac{1}{3}}}=\frac{1}{2}[{1-{{£¨\frac{1}{3}£©}^n}}]$£¬ÓÉ$1-{£¨\frac{1}{3}£©^n}£¼1$£¬Ôò$\frac{1}{2}[{1-{{£¨\frac{1}{3}£©}^n}}]£¼\frac{1}{2}$£¬¼´¿ÉÖ¤Ã÷${S_n}£¼\frac{1}{2}$£»
£¨2£©${b_n}={log_{\frac{1}{3}}}{a_1}+{log_{\frac{1}{3}}}{a_2}+¡­+{log_{\frac{1}{3}}}{a_n}={log_{\frac{1}{3}}}£¨{a_1}{a_2}¡­{a_n}£©$=${log_{\frac{1}{3}}}{£¨\frac{1}{3}£©^{1+2+¡­+n}}$=$1+2+¡­+n=\frac{n£¨1+n£©}{2}$£¬Ôò$\frac{1}{b_n}=\frac{2}{n£¨1+n£©}=2£¨\frac{1}{n}-\frac{1}{n+1}£©$£¬²ÉÓá°ÁÑÏî·¨¡±¼´¿ÉÇóµÃTn£®

½â´ð ½â£º£¨1£©µ±n¡Ý2ʱ£¬Sn-1=$\frac{1}{2}$£¨1-an-1£©£¬an=Sn-Sn-1£¬
¡à${a_n}=\frac{1}{2}£¨1-{a_n}£©-\frac{1}{2}£¨1-{a_{n-1}}£©$=$-\frac{1}{2}{a_n}+\frac{1}{2}{a_{n-1}}$£¬ÕûÀíµÃ£º2an=-an+an-1£¬
¡à$\frac{a_n}{{{a_{n-1}}}}=\frac{1}{3}$£¬
µ±n=1ʱ£¬
${S_1}={a_1}=\frac{1}{2}£¨1-{a_1}£©$£¬½âµÃ£º${a_1}=\frac{1}{3}$£¬
¡àÊýÁÐ{an}ÊÇÊ×Ïî${a_1}=\frac{1}{3}$£¬¹«±ÈΪ$\frac{1}{3}$µÄµÈ±ÈÊýÁУ¬
¡à${a_n}=\frac{1}{3}¡Á{£¨\frac{1}{3}£©^{n-1}}={£¨\frac{1}{3}£©^n}$£¬
Ö¤Ã÷£ºÓɵȱÈÊýÁÐǰnÏʽ¿ÉÖª£º${S_n}=\frac{{\frac{1}{3}[{1-{{£¨\frac{1}{3}£©}^n}}]}}{{1-\frac{1}{3}}}=\frac{1}{2}[{1-{{£¨\frac{1}{3}£©}^n}}]$£¬
¡ß$1-{£¨\frac{1}{3}£©^n}£¼1$£¬
¡à$\frac{1}{2}[{1-{{£¨\frac{1}{3}£©}^n}}]£¼\frac{1}{2}$£¬
¡à${S_n}£¼\frac{1}{2}$£®
£¨2£©¡ß$f£¨x£©={log_{\frac{1}{3}}}x$£¬
¡à${b_n}={log_{\frac{1}{3}}}{a_1}+{log_{\frac{1}{3}}}{a_2}+¡­+{log_{\frac{1}{3}}}{a_n}={log_{\frac{1}{3}}}£¨{a_1}{a_2}¡­{a_n}£©$=${log_{\frac{1}{3}}}{£¨\frac{1}{3}£©^{1+2+¡­+n}}$£¬
=$1+2+¡­+n=\frac{n£¨1+n£©}{2}$£®
¡ß$\frac{1}{b_n}=\frac{2}{n£¨1+n£©}=2£¨\frac{1}{n}-\frac{1}{n+1}£©$£¬
¡à${T_n}=\frac{1}{b_1}+\frac{1}{b_2}+¡­+\frac{1}{b_n}=2[{£¨1-\frac{1}{2}£©+£¨\frac{1}{2}-\frac{1}{3}£©+¡­+£¨\frac{1}{n}-\frac{1}{n+1}£©}]=\frac{2n}{n+1}$£¬
¡àTn=$\frac{2n}{n+1}$£®

µãÆÀ ±¾Ì⿼²éµÈ±ÈÊýÁÐǰnÏîºÍ¹«Ê½µÄÓ¦Óã¬ÇóµÈ²îÊýÊýÁеÄǰnÏîºÍ£¬¿¼²é¡°ÁÑÏî·¨¡±ÇóÊýÁеÄǰnÏîºÍ£¬¿¼²é¼ÆËãÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

20£®ÒÑÖªÃüÌâp£ºº¯Êýy=mx2-6x+2ÓÐÁãµã£»ÃüÌâq£ºº¯Êýf£¨x£©=x2+2mx+1ÔÚ[-2£¬5]ÉÏÊǵ¥µ÷º¯Êý£»
Èô¡°p»òq¡±ÎªÕæÃüÌ⣬¡°pÇÒq¡±Îª¼ÙÃüÌ⣬ÇóʵÊýmµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

1£®ÒÑÖª´¹Ö±ÊúÔÚˮƽµØÃæÉÏÏà¾à20Ã×µÄÁ½¸ùÆì¸ËµÄ¸ß¶È·Ö±ðΪ10Ã׺Í15Ã×£¬µØÃæÉϵ͝µãPµ½Á½Æì¸Ë¶¥µãµÄÑö½ÇÏàµÈ£¬ÔòµãPµÄ¹ì¼£ÊÇÔ²£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

18£®ÒÑÖªÊýÁÐ{an}µÄǰnÏîºÍSn=$\frac{n+1}{n+2}$£¬Ôòa4=£¨¡¡¡¡£©
A£®$\frac{1}{20}$B£®$\frac{1}{30}$C£®1D£®$\frac{7}{30}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

5£®Éè2016¡Ê{x£¬$\sqrt{{x}^{2}}$£¬x2}£¬ÔòÂú×ãÌõ¼þµÄËùÓÐx×é³ÉµÄ¼¯ºÏµÄÕæ×Ó¼¯µÄ¸öÊýÊÇ15¸ö£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

15£®½â²»µÈʽax2-£¨a-1£©x-1¡Ü0£¨a¡ÊR£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

2£®ÍÖÔ²$\frac{x^2}{{{{10}^{\;}}}}+\frac{y^2}{{{m^{\;}}}}=1$µÄ½¹¾àΪ6£¬ÔòmµÄֵΪ£¨¡¡¡¡£©
A£®m=1B£®m=19C£®m=1 »ò m=19D£®m=4»òm=16

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

19£®ÒÑÖªº¯Êýf£¨x£©=-x2+ax+bµÄÖµÓòΪ£¨-¡Þ£¬0]£¬Èô¹ØxµÄ²»µÈʽ$f£¨x£©£¾-\frac{c}{4}-1$µÄ½â¼¯Îª£¨m-4£¬m+1£©£¬ÔòʵÊýcµÄֵΪ21£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

20£®Èçͼ£¬Á½¸öÍÖÔ²$\frac{{x}^{2}}{25}$+$\frac{{y}^{2}}{9}$=1£¬$\frac{{y}^{2}}{25}$+$\frac{{x}^{2}}{9}$=1ÄÚ²¿ÖصþÇøÓòµÄ±ß½ç¼ÇΪÇúÏßC£¬PÊÇÇúÏßCÉÏÈÎÒâÒ»µã£¬¸ø³öÏÂÁÐÈý¸öÅжϣº
¢ÙPµ½F1£¨-4£¬0£©¡¢F2£¨4£¬0£©¡¢E1£¨0£¬-4£©¡¢E2£¨0£¬4£©ËĵãµÄ¾àÀëÖ®ºÍΪ¶¨Öµ£»
¢ÚÇúÏßC¹ØÓÚÖ±Ïßy=x¡¢y=-x¾ù¶Ô³Æ£»
¢ÛÇúÏßCËùÎ§ÇøÓòÃæ»ý±ØÐ¡ÓÚ36£®
ÉÏÊöÅжÏÖÐÕýÈ·ÃüÌâµÄ¸öÊýΪ£¨¡¡¡¡£©
A£®0¸öB£®1¸öC£®2¸öD£®3¸ö

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸