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hylpy
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hylpy: ½ð±Ò+2, Èç¹ûÖØÐ±àһϣ¬¾Í¸üºÃÁË 2015-11-15 19:15:57
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hylpy: ½ð±Ò+2, Èç¹ûÖØÐ±àһϣ¬¾Í¸üºÃÁË 2015-11-15 19:15:57
Edstrayer: ½ð±Ò+5, LatexÔ´Îļþ±àÒëͨ¹ý£¬µ«²»·ûºÏСľ³æÂÛ̳µÄ¸ñʽ£¬¹ÄÀøÒ»Ï 2015-11-16 17:25:39
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ÎÒÔÚLATEXÀïÃæ±à¼µÄ£¬ËùÒÔÖ»ÓдúÂë Ҫ˯¾õÁË£¬ËùÒÔ¸ñʽҲû¸Ä£¬¼ûÁ Æäʵ˼·¾ÍÊÇÓõ¥µ÷ÓнçÊýÁбØÓм«ÏÞÕâ¸ö×¼Ôò GOOD NIGHT \documentclass{article} \usepackage{amsmath} \usepackage{amssymb} \begin{document} \par{$$\because 0<a_{1}<7,0<a_{2}<7$$} \par{$$\because a_{n+2}=\sqrt{7-\sqrt{7+a_{n}}}$$} \par{$$\therefore 0<a_{2n+1}<7,0<a_{2n+1}<7$$} \par{$$\therefore 0<a_{n}<7$$} \par{$$\therefore \{a_{n}\} is\quad bounded.$$} \par{quad} \par{$$\because a_{n+2}=\sqrt{7-\sqrt{7+a_{n}}}$$} \par{$$\therefore a_{4n+i}-a_{4(n-1)+i}=\sqrt{7-\sqrt{7+a_{4n+i-2}}}-\sqrt{7-\sqrt{7+a_{4(n-1)+i-2}}}=\frac{\sqrt{7+a_{4(n-1)+i-2}}-\sqrt{7+a_{4n+i-2}}}{a_{4n+i}+a_{4(n-1)+i}},i=0,1,2,3$$} \par{$$\therefore a_{4n+i}-a_{4(n-1)+i}=k(a_{4(n-1)+i}-a_{4(n-2)+i}),k>0;i=0,1,2,3$$} \par{$$\therefore \{a_{4n+i}\} is\quad monotone\quad decreasing.(i=0,1,2,3)$$} \par{$$\therefore \{a_{4n+i}\} is\quad Convergent\quad sequence.(i=0,1,2,3)$$} \par{\quad} \par{$$Suppose\quad \lim_{n\rightarrow\infty} a_{4n+i}=A$$} \par{$$\because a_{n+2}=\sqrt{7-\sqrt{7+a_{n}}}$$} \par{$$\therefore A=\sqrt{7-\sqrt{7+\sqrt{7-\sqrt{7+A}}}}$$} \par{$$\therefore A=-3,2,\frac{1\pm\sqrt{29}}{2} ......$$} \par{$$\because 0\leq a_{n}\leq\sqrt{7}$$} \par{$$\therefore 0\leq A\leq\sqrt{7}$$} \par{$$\therefore A=2$$} \par{.....} \end{document} |
2Â¥2015-11-14 23:42:01
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Edstrayer
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maojun1998
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10Â¥2015-11-15 16:54:42
hylpy
ר¼Ò¹ËÎÊ (ÖªÃû×÷¼Ò)
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12Â¥2015-11-15 19:07:49
hylpy
ר¼Ò¹ËÎÊ (ÖªÃû×÷¼Ò)
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13Â¥2015-11-15 19:11:20
14Â¥2015-11-15 21:25:56
maojun1998
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15Â¥2015-11-15 23:03:49
hylpy
ר¼Ò¹ËÎÊ (ÖªÃû×÷¼Ò)
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17Â¥2015-11-19 08:30:01
34Â¥2015-11-19 08:55:38
tableman
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