11£®ÒÑÖªÔÚÊýÁÐ{an}ÖУ¬a1=1£¬ÆäǰnÏîºÍΪsn£¬ÇÒ${a_n}=\frac{2s_n^2}{{2{s_n}-1}}$£¨n¡Ý2£©
£¨1£©Ö¤Ã÷$\left\{{\frac{1}{s_n}}\right\}$ÊǵȲîÊýÁУ¬²¢ÇóÊýÁÐ$\left\{{\frac{1}{s_n}}\right\}$µÄǰnÏîºÍPn
£¨2£©Èô${b_n}=\frac{s_n}{2n+1}+\frac{2^n}{s_n}$ÇóÊýÁеÄǰÏîºÍTn£®

·ÖÎö £¨1£©µ±n¡Ý2ʱ£¬${a_n}={s_n}-{s_{n-1}}=\frac{2s_n^2}{{2{s_n}-1}}$£¬»¯¼òµÃsn-1-sn=2snsn-1£¬ÀûÓõȲîÊýÁеÄͨÏʽÓëÇóºÍ¹«Ê½¼´¿ÉµÃ³ö£®
£¨2£©ÓÉ£¨1£©¿ÉµÃSn£¬ÔÙÀûÓá°´íλÏà¼õ·¨¡±ÓëµÈ±ÈÊýÁеÄÇóºÍ¹«Ê½¼´¿ÉµÃ³ö£®

½â´ð ½â£º£¨1£©Ö¤Ã÷£ºµ±n¡Ý2ʱ£¬${a_n}={s_n}-{s_{n-1}}=\frac{2s_n^2}{{2{s_n}-1}}$£¬
»¯¼òµÃsn-1-sn=2snsn-1£¬¼´$\frac{1}{s_n}-\frac{1}{{{s_{n-1}}}}=2$£¬ÓÖ$\frac{1}{s_1}=\frac{1}{a_1}=1$£¬
ËùÒÔÊýÁÐ$\left\{{\frac{1}{s_n}}\right\}$ΪÒÔ1ΪÊ×Ï2Ϊ¹«²îµÄµÈ²îÊýÁУ¬
$\frac{1}{s_n}=2n-1$£¬ÔòPn=$\frac{£¨1+2n-1£©•n}{2}$=n2£®
£¨2£©ÓÉ£¨1£©µÃ$\frac{1}{s_n}=2n-1$£¬
ËùÒÔ${s_n}=\frac{1}{2n-1}$£¬${b_n}=\frac{s_n}{2n+1}+\frac{2^n}{s_n}=\frac{1}{£¨2n-1£©£¨2n+1£©}+£¨2n-1£©¡Á{2^n}$
=$\frac{1}{2}£¨\frac{1}{2n-1}-\frac{1}{2n+1}£©+£¨2n-1£©¡Á{2^n}$£¬
ËùÒÔ${A_n}=\frac{1}{2}£¨1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+¡­+\frac{1}{2n-1}-\frac{1}{2n+1}£©=\frac{n}{2n+1}$${B_n}=1¡Á2+3¡Á{2^2}+5¡Á{2^3}+¡­+£¨2n-3£©¡Á{2^{n-1}}+£¨2n-1£©¡Á{2^n}$£¬¢Ù$2{B_n}=1¡Á{2^2}+3¡Á{2^3}+5¡Á{2^4}+¡­+£¨2n-3£©¡Á{2^n}+£¨2n-1£©¡Á{2^{n+1}}$£¬¢Ú
¢Ù-¢ÚµÃ£¬$-{B_n}=1¡Á2+2¡Á{2^2}+2¡Á{2^3}+¡­+2¡Á{2^{n-1}}+2¡Á{2^n}-£¨2n-1£©¡Á{2^{n+1}}$
=£¨3-2n£©¡Á2n+1-6£¬
¡à${T_n}={A_n}+{B_n}=\frac{n}{2n+1}+£¨2n-3£©¡Á{2^{n+1}}+6$£®

µãÆÀ ±¾Ì⿼²éÁËÊýÁеÝÍÆ¹ØÏµ¡¢¡°´íλÏà¼õ·¨¡±¡¢µÈ²îÊýÁÐÓëµÈ±ÈÊýÁеÄͨÏʽÓëÇóºÍ¹«Ê½£¬¿¼²éÁËÍÆÀíÄÜÁ¦Óë¼ÆËãÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

1£®ÒÑÖªF1£¬F2ÊÇË«ÇúÏß$\frac{{x}^{2}}{{a}^{2}}$-$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾0£¬b£¾0£©µÄ×ó¡¢ÓÒ½¹µã£¬ÉèË«ÇúÏßµÄÀëÐÄÂÊΪe£®ÈôÔÚË«ÇúÏßµÄÓÒÖ§ÉÏ´æÔÚµãM£¬Âú×ã|MF2|=|F1F2|£¬ÇÒesin¡ÏMF1F2=1£¬Ôò¸ÃË«ÇúÏßµÄÀëÐÄÂÊeµÈÓÚ£¨¡¡¡¡£©
A£®$\frac{5}{4}$B£®$\frac{5}{3}$C£®$\sqrt{5}$D£®$\frac{5}{2}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

2£®ÒÑÖªÏòÁ¿$\overrightarrow a=£¨1£¬-1£©£¬\overrightarrow b=£¨x£¬2£©$£¬ÇÒ$\overrightarrow a¡Í\overrightarrow b$£¬Ôò$|{\overrightarrow a+\overrightarrow b}|$µÄֵΪ£¨¡¡¡¡£©
A£®$\sqrt{2}$B£®$\sqrt{7}$C£®$2\sqrt{2}$D£®$\sqrt{10}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

19£®É躯Êýf£¨x£©=x2+ax+b£¨a£¬b¡ÊR£©µÄÁ½¸öÁãµãΪx1£¬x2£¬Èô|x1|+|x2|¡Ü2£¬Ôò£¨¡¡¡¡£©
A£®|a|¡Ý1B£®b¡Ü1C£®|a+2b|¡Ý2D£®|a+2b|¡Ü2

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

6£®ÒÑÖªÈýÀâ×¶A-BCDµÄËĸö¶¥µãA£¬B£¬C£¬D¶¼ÔÚÇòOµÄ±íÃæÉÏ£¬BC¡ÍCD£¬AC¡ÍÆ½ÃæBCD£¬ÇÒAC=2$\sqrt{2}$£¬BC=CD=2£¬ÔòÇòOµÄ±íÃæ»ýΪ£¨¡¡¡¡£©
A£®4¦ÐB£®8¦ÐC£®16¦ÐD£®2$\sqrt{2}$¦Ð

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

16£®¡°|a|£¾|b|¡±ÊÇ¡°lna£¾lnb¡±µÄ£¨¡¡¡¡£©
A£®³äÒªÌõ¼þB£®³ä·Ö²»±ØÒªÌõ¼þ
C£®±ØÒª²»³ä·ÖÌõ¼þD£®¼È²»³ä·ÖÒ²²»±ØÒªÌõ¼þ

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

3£®ÒÑÖªº¯Êýf£¨x£©=|x-a|£®
£¨1£©Èôa=1£¬½â²»µÈʽf£¨x£©¡Ý4-|x+1|£»
£¨2£©Èô²»µÈʽf£¨x£©¡Ü1µÄ½â¼¯Îª$[{0£¬2}]£¬\frac{1}{m}+\frac{1}{2n}=a£¨{m£¾0£¬n£¾0}£©$£¬ÇómnµÄ×îСֵ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

20£®ÒÑÖªÏòÁ¿$\overrightarrow a$£¬$\overrightarrow b$Âú×ã$|\overrightarrow a|=1$£¬$|\overrightarrow b|=2$£¬$|\overrightarrow a+\overrightarrow b|=\sqrt{5}$£¬Ôò$|2\overrightarrow a-\overrightarrow b|$=2$\sqrt{2}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

1£®ÒÑÖª¼¯ºÏU={-1£¬0£¬1}£¬B={x|x=m2£¬m¡ÊU}£¬Ôò∁UB=£¨¡¡¡¡£©
A£®{0£¬1}B£®{-1£¬0£¬1}C£®D£®{-1}

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸