·ÖÎö £¨¢ñ£©Ö±½ÓÓÉÊýÁеÄǰnÏîºÍÇóµÃÊýÁÐͨÏʽ£»
£¨¢ò£©ÓÉbn=$\frac{{a}_{n}}{{2}^{n}}$£¬È»ºóÀûÓÃÁÑÏîÏàÏû·¨ÇóÊýÁÐ{bn}µÄǰnÏîºÍTn£»
£¨¢ó£©°Ñ¸ø³öµÄ²»µÈʽ±äÐΣ¬µÃµ½p¡Ü$\frac{1}{\sqrt{2n+1}}$£¨1+$\frac{1}{{a}_{1}}$£©£¨1+$\frac{1}{{a}_{2}}$£©¡£¨1+$\frac{1}{{a}_{n}}$£©¶Ôn¡ÊN*ºã³ÉÁ¢£¬¼Çf£¨n£©=$\frac{1}{\sqrt{2n+1}}$£¨1+$\frac{1}{{a}_{1}}$£©£¨1+$\frac{1}{{a}_{2}}$£©¡£¨1+$\frac{1}{{a}_{n}}$£©£¬ÓÉ×÷ÉÌ·¨ÇóµÃÆäµ¥µ÷ÐԿɵÃ×î´óʵÊýpµÄÖµ£®
½â´ð ½â£º£¨¢ñ£©ÓÉ${S_n}={n^2}$£¬µÃa1=1£»µ±n¡Ý2ʱ£¬${a}_{n}={S}_{n}-{S}_{n-1}={n}^{2}-£¨n-1£©^{2}=2n-1$£®
ÑéÖ¤n=1ʱÉÏʽ³ÉÁ¢£¬¡àÊýÁÐ{an}µÄͨÏʽan=2n-1£»
£¨¢ò£©bn=$\frac{{a}_{n}}{{2}^{n}}$=$\frac{2n-1}{{2}^{n}}$£¬
¡àTn=$\frac{1}{{2}^{1}}+\frac{3}{{2}^{2}}+\frac{5}{{2}^{3}}+¡+\frac{2n-1}{{2}^{n}}$£¬¢Ù
$\frac{1}{2}{T}_{n}=\frac{1}{{2}^{2}}+\frac{3}{{2}^{3}}+¡+\frac{2n-3}{{2}^{n}}+\frac{2n-1}{{2}^{n+1}}$£¬¢Ú
¢Ù-¢ÚµÃ£º$\frac{1}{2}{T}_{n}=\frac{1}{2}+\frac{1}{2}+\frac{1}{{2}^{2}}+¡+\frac{1}{{2}^{n-1}}-\frac{2n-1}{{2}^{n+1}}$=$\frac{1}{2}+\frac{\frac{1}{2}£¨1-\frac{1}{{2}^{n-1}}£©}{1-\frac{1}{2}}-\frac{2n-1}{{2}^{n+1}}$=$\frac{3}{2}-\frac{1}{{2}^{n-1}}-\frac{2n-1}{{2}^{n+1}}$£¬
¡à${T}_{n}=3-\frac{2n+3}{{2}^{n}}$£»
£¨¢ó£©ÓÉÌâÒâµÃp¡Ü$\frac{1}{\sqrt{2n+1}}$£¨1+$\frac{1}{{a}_{1}}$£©£¨1+$\frac{1}{{a}_{2}}$£©¡£¨1+$\frac{1}{{a}_{n}}$£©¶Ôn¡ÊN*ºã³ÉÁ¢£¬
¼Çf£¨n£©=$\frac{1}{\sqrt{2n+1}}$£¨1+$\frac{1}{{a}_{1}}$£©£¨1+$\frac{1}{{a}_{2}}$£©¡£¨1+$\frac{1}{{a}_{n}}$£©£¬
Ôò$\frac{f£¨n+1£©}{f£¨n£©}$=$\frac{\frac{1}{\sqrt{2n+3}}£¨1+\frac{1}{{a}_{1}}£©£¨1+\frac{1}{{a}_{2}}£©¡£¨1+\frac{1}{{a}_{n+1}}£©}{\frac{1}{\sqrt{2n+1}}£¨1+\frac{1}{{a}_{1}}£©£¨1+\frac{1}{{a}_{2}}£©¡£¨1+\frac{1}{{a}_{n}}£©}$
=$\frac{2n+2}{\sqrt{2n+1}\sqrt{2n+3}}$=$\frac{2£¨n+1£©}{\sqrt{4£¨n+1£©^{2}-1}}$£¾$\frac{2£¨n+1£©}{2£¨n+1£©}$=1£®
¡ßf£¨n£©£¾0£¬
¡àf£¨n+1£©£¾f£¨n£©£¬
¼´f£¨n£©ÊÇËænµÄÔö´ó¶øÔö´ó£¬f£¨n£©µÄ×îСֵΪf£¨1£©=$\frac{2\sqrt{3}}{3}$£¬
¡àʵÊýpµÄ×î´óֵΪ$\frac{2\sqrt{3}}{3}$£®
µãÆÀ ±¾Ì⿼²éµÄ֪ʶµãÊǵȲîÊýÁе͍Ò弰ͨÏʽ£¬µÈ±ÈÊýÁе͍Òå¼°Åж¨·½·¨£¬ÊýÁеĵÝÍÆ¹«Ê½£¬ºã³ÉÁ¢ÎÊÌ⣬ÊÇÊýÁÐÓ뺯ÊýµÄ×ÛºÏÓ¦Óã¬ÄѶȽϴó£®
| Äê¼¶ | ¸ßÖÐ¿Î³Ì | Äê¼¶ | ³õÖÐ¿Î³Ì |
| ¸ßÒ» | ¸ßÒ»Ãâ·Ñ¿Î³ÌÍÆ¼ö£¡ | ³õÒ» | ³õÒ»Ãâ·Ñ¿Î³ÌÍÆ¼ö£¡ |
| ¸ß¶þ | ¸ß¶þÃâ·Ñ¿Î³ÌÍÆ¼ö£¡ | ³õ¶þ | ³õ¶þÃâ·Ñ¿Î³ÌÍÆ¼ö£¡ |
| ¸ßÈý | ¸ßÈýÃâ·Ñ¿Î³ÌÍÆ¼ö£¡ | ³õÈý | ³õÈýÃâ·Ñ¿Î³ÌÍÆ¼ö£¡ |
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ
| A£® | 1 | B£® | $\frac{5}{3}$ | C£® | 2 | D£® | $\frac{7}{3}$ |
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ
| A£® | c£¾a£¾b | B£® | a£¾c£¾b | C£® | a£¾b£¾c | D£® | b£¾a£¾c |
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ
| A£® | ³ä·ÖÌõ¼þµ«·Ç±ØÒªÌõ¼þ | B£® | ±ØÒªÌõ¼þµ«·Ç³ä·ÖÌõ¼þ | ||
| C£® | ³ä·Ö±ØÒªÌõ¼þ | D£® | ·Ç³ä·ÖÌõ¼þ£¬Ò²·Ç±ØÒªÌõ¼þ |
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¹ú¼ÊѧУÓÅÑ¡ - Á·Ï°²áÁбí - ÊÔÌâÁбí
ºþ±±Ê¡»¥ÁªÍøÎ¥·¨ºÍ²»Á¼ÐÅÏ¢¾Ù±¨Æ½Ì¨ | ÍøÉÏÓк¦ÐÅÏ¢¾Ù±¨×¨Çø | µçÐÅթƾٱ¨×¨Çø | ÉæÀúÊ·ÐéÎÞÖ÷ÒåÓк¦ÐÅÏ¢¾Ù±¨×¨Çø | ÉæÆóÇÖȨ¾Ù±¨×¨Çø
Î¥·¨ºÍ²»Á¼ÐÅÏ¢¾Ù±¨µç»°£º027-86699610 ¾Ù±¨ÓÊÏ䣺58377363@163.com