15£®ÒÑÖªÊýÁÐ{an}µÄÇ°nÏîºÍΪSn£¬ÇÒÂú×ãan+Sn=$\frac{1}{2}$£¨n2+3n£©£¬ÊýÁÐ{bn}Âú×ãbn=$\sqrt{1+\frac{1}{{{a}_{n}}^{2}}+\frac{1}{{{a}_{n+1}}^{2}}}$£¬ÊýÁÐ{bn}µÄÇ°nÏîºÍΪTn£¬MΪÕýÕûÊý£®
£¨1£©ÇóÊýÁÐ{an}µÄͨÏʽan£»
£¨2£©ÈôÊýÁÐ{bn}µÄÇ°2015ÏîµÄºÍT2015¡ÝM£¬ÇóMµÄ×î´óÖµ£®

·ÖÎö £¨1£©ÔËÓÃan=$\left\{\begin{array}{l}{{S}_{1}£¬n=1}\\{{S}_{n}-{S}_{n-1}£¬n£¾1}\end{array}\right.$£¬ÇóµÃa1=1£¬a2=2£¬¹¹ÔìÊýÁеķ½·¨¿ÉµÃan-n=$\frac{1}{2}$[an-1-£¨n-1£©]£¬¼´¿ÉµÃµ½ËùÇóͨÏ
£¨2£©»¯¼òbn=$\sqrt{\frac{{n}^{2}£¨n+1£©^{2}+£¨n+1£©^{2}+{n}^{2}}{{n}^{2}£¨n+1£©^{2}}}$=$\frac{n£¨n+1£©+1}{n£¨n+1£©}$=1+$\frac{1}{n£¨n+1£©}$=1+$\frac{1}{n}$-$\frac{1}{n+1}$£¬ÓÉÁÑÏîÏàÏûÇóºÍ£¬¿ÉµÃÇ°2015ÏîµÄºÍT2015=2016-$\frac{1}{2016}$£¬¼´¿ÉµÃµ½ËùÇóÖµ£®

½â´ð ½â£º£¨1£©an+Sn=$\frac{1}{2}$£¨n2+3n£©£¬¢Ù¿ÉµÃa1+S1=2a1=2£¬
½âµÃa1=1£¬ÓÖa2+S2=$\frac{1}{2}$£¨22+6£©=5£¬½âµÃa2=2£¬
µ±n£¾1ʱ£¬an-1+Sn-1=$\frac{1}{2}$[£¨n-1£©2+3£¨n-1£©]£¬¢Ú
¢Ù-¢Ú£¬¿ÉµÃ2an-an-1=n+1£¬
±äÐÎΪan-n=$\frac{1}{2}$[an-1-£¨n-1£©]£¬
ÓÉÓÚa1-1=a2-2=0£¬Ôòan-n=0£¬
¹ÊÊýÁÐ{an}µÄͨÏʽan=n£»
£¨2£©bn=$\sqrt{1+\frac{1}{{{a}_{n}}^{2}}+\frac{1}{{{a}_{n+1}}^{2}}}$=$\sqrt{1+\frac{1}{{n}^{2}}+\frac{1}{£¨n+1£©^{2}}}$
=$\sqrt{\frac{{n}^{2}£¨n+1£©^{2}+£¨n+1£©^{2}+{n}^{2}}{{n}^{2}£¨n+1£©^{2}}}$=$\frac{n£¨n+1£©+1}{n£¨n+1£©}$=1+$\frac{1}{n£¨n+1£©}$=1+$\frac{1}{n}$-$\frac{1}{n+1}$£¬
Ç°2015ÏîµÄºÍT2015=£¨1+1-$\frac{1}{2}$£©+£¨1+$\frac{1}{2}$-$\frac{1}{3}$£©+£¨1+$\frac{1}{3}$-$\frac{1}{4}$£©+¡­+£¨1+$\frac{1}{2015}$-$\frac{1}{2016}$£©
=2016-$\frac{1}{2016}$£¬
¹Ê²»³¬¹ýT2015µÄ×î´óÕûÊýMΪ2015£®

µãÆÀ ±¾Ì⿼²éÊýÁеÄͨÏîµÄÇ󷨣¬×¢ÒâÔËÓÃan=$\left\{\begin{array}{l}{{S}_{1}£¬n=1}\\{{S}_{n}-{S}_{n-1}£¬n£¾1}\end{array}\right.$£¬ÒÔ¼°¹¹ÔìÊýÁеÄ˼Ïë·½·¨£¬¿¼²éÁÑÏîÏàÏûÇóºÍµÄ˼Ï룬¿¼²éÔËËãÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

5£®º¯Êýy=sin£¨2x-1£©µÄͼÏó¿ÉÓɺ¯Êýy=sin£¨2x+1£©µÄͼÏóÏòÓÒƽÒÆ1¸öµ¥Î»³¤¶È¶øµÃµ½£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

6£®ËµÃ÷Óɺ¯Êýy=sinxµÄͼÏó¾­¹ýÔõÑùµÄ±ä»»¾ÍÄܵõ½ÏÂÁк¯ÊýµÄͼÏó£º
£¨1£©y=sin£¨x+$\frac{¦Ð}{4}$£©£» 
£¨2£©y=sin£¨2x-$\frac{¦Ð}{3}$£©£»
£¨4£©y=5sin£¨3x-$\frac{¦Ð}{4}$£©£»
£¨3£©y=$\frac{1}{2}$sin£¨$\frac{1}{3}$x+$\frac{¦Ð}{6}$£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

3£®ÒÑÖªº¯Êýf£¨x£©=xlnx£¬g£¨x£©=£¨-x2+ax-3£©ex£¨aΪʵÊý£©
£¨1£©Çóf£¨x£©µÄµ¥µ÷ÔöÇø¼ä£»
£¨2£©Çóº¯Êýf£¨x£©ÔÚÇø¼ä[t£¬t+1]£¨t£¾0£©ÉϵÄ×îСֵh£¨t£©£»
£¨3£©Èô¶ÔÈÎÒâx¡Ê[$\frac{1}{e}$£¬e]£¬¶¼ÓÐg£¨x£©¡Ý2exf£¨x£©³ÉÁ¢£¬ÇóʵÊýaµÄÈ¡Öµ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

10£®»­³öÒÔ¶þÔªÒ»´Î²»µÈʽx+2y-5£¼0µÄ½âΪ×ø±êµÄµãÔÚƽÃæÖ±½Ç×ø±êϵÖеÄͼÐΣ®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

20£®ÒÑÖª¼¯ºÏA={1£¬2}ÓëB={x|x2+px+q=0}£¬ÇÒA¡ÈB=B£¬ÇóʵÊýpºÍqµÄÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

7£®ÒÑÖªa=2-1£¬b=${3}^{\frac{1}{5}}$£¬c=${3}^{\frac{4}{5}}$£¬Ôòa£¬b£¬cµÄ´óС¹ØϵÊÇ£¨¡¡¡¡£©
A£®a£¼b£¼cB£®b£¼c£¼aC£®c£¼a£¼bD£®a£¼c£¼b

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

4£®Éèf£¨x£©=3x£¬g£¨x£©=£¨$\frac{1}{3}$£©x£®
£¨1£©ÔÚͬһ×ø±êϵÖÐ×÷³öf£¨x£©£¬g£¨x£©µÄͼÏó£®
£¨2£©¼ÆËãf£¨1£©Óëg£¨-1£©£¬f£¨¦Ð£©Óëg£¨-¦Ð£©£¬f£¨m£©Óëg£¨-m£©µÄÖµ£¬´ÓÖÐÄãÄܵõ½Ê²Ã´½áÂÛ£¿

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

1£®£¨Àí¿Æ£©ÔÚÕý·½ÌåABCD-A1B1C1D1ÖУ¬E£¬FΪA1B1£¬CC1µÄÖе㣬ÔòÒìÃæÖ±ÏßD1EºÍBFËù³É½ÇµÄÓàÏÒֵΪ£¨¡¡¡¡£©
A£®$\frac{4}{5}$B£®-$\frac{4}{5}$C£®$\frac{16}{25}$D£®-$\frac{16}{25}$

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸