Question

19£®ÓñÃ×£¨2n=20£©Ò¶Æ¬Ò¶ÂÌËصĺϳÉÊÜϸ°ûºËÖÐÒ»¶ÔµÈλ»ùÒò£¨A¡¢a£©µÄ¿ØÖÆ£®ÔÚÓñÃ×Ö²ÖêÖУ¬»ùÒòÐÍΪAAµÄÖ²ÖêҶƬ³ÊÉîÂÌÉ«£¬AaÖ²ÖêҶƬ³ÊdzÂÌÉ«£¬Ã»ÓÐA»ùÒòµÄÖ²ÖêҶƬ³Êdz»ÆÉ«£¬»áÔÚÓ×ÃçÆÚºóËÀÍö£®ÓÐÒ»ÅúdzÂÌÉ«Ö²ÖêÇ×±¾£¬Èç¹ûÈÃËüÃÇÏ໥Êڷ۵õ½F₁£¬F₁Ö²Öê¼ä×ÔÓÉÊڷ۵õ½F₂£¬¡­Öð´ú×ÔÓÉÊڷ۵õ½F_n£¬ÄÇôÔÚF_n´ú³ÉÊìÖ²ÖêÖÐa»ùÒòƵÂÊΪ£¨¡¡¡¡£©

• A£® $\frac{1}{2}$
• B£® $\frac{1}{£¨2n+1£©}$
• C£® $\frac{1}{£¨n+2}£©$
• D£® £¨$\frac{1}{2}$£©ⁿ

Answer 1

·ÖÎö 1¡¢»ùÒò·ÖÀ붨ÂɵÄʵÖÊ£º½øÐÐÓÐÐÔÉúÖ³µÄÉúÎïÔÚ½øÐмõÊý·ÖÁѹý³ÌÖУ¬Í¬Ô´È¾É«ÌåÉϵĵÈλ»ùÒòËæͬԴȾɫÌå·ÖÀë¶ø·ÖÀ룬·Ö±ð½øÈ벻ͬµÄÅä×ÓÖУ¬ËæÅä×Ó¶ÀÁ¢ÒÅ´«¸øºó´ú£»Ö²Öê½øÐÐ×ÔÓÉÊÚ·ÛÊôÓÚ×ÔÓɽ»Å䣬¿ÉÒÔÏȼÆËã´ÆÐÛÅä×ÓµÄÀàÐͼ°±ÈÀý£¬È»ºó°´ÕÕ´ÆÐÛÅä×ÓËæ»ú½áºÏ¼ÆËã×ÔÓɽ»Åäºó´úµÄ»ùÒòÐͼ°±ÈÀý£®
2¡¢¸ù¾Ý»ùÒòÐÍƵÂʼÆËã»ùÒòƵÂʵķ½·¨£ºÏÔÐÔ»ùÒòµÄ»ùÒòƵÂÊ=ÏÔÐÔ´¿ºÏ×ӵĻùÒòÐÍƵÂÊ+ÔÓºÏ×Ó»ùÒòÐÍƵÂÊ¡Â2£¬ÒþÐÔ»ùÒòµÄ»ùÒòƵÂÊ=ÒþÐÔ´¿ºÏ×ӵĻùÒòÐÍƵÂÊ+ÔÓºÏ×Ó»ùÒòÐÍƵÂÊ¡Â2£®

½â´ð ½â£ºÓÉÌâÒâÖª£¬Ç³ÂÌÉ«Ö²ÖêÇ×±¾µÄ»ùÒòÐÍÊÇAa£¬×ÔÓɽ»ÅäÏ൱ÓÚ×Ô½»£¬ºó´úµÄ»ùÒòÐͼ°±ÈÀýÊÇAA£ºAa£ºaa=1£º2£º1£¬ÓÉÓÚaaÓ×ÃçÆÚËÀÍö£¬Òò´Ë³ÉÊìÖ²Öê»ùÒòÐͱÈÀýÊÇAA£ºAa=1£º2£¬aµÄ»ùÒòƵÂÊÊÇa=$\frac{2}{3}¡Á\frac{1}{2}=\frac{1}{3}$£»×ÓÒ»´ú²úÉúµÄÅä×ÓµÄÀàÐͼ°±ÈÀýÊÇA£ºa=2£º1£¬ÓÉÓÚ´ÆÐÛÅä×Ó½áºÏÊÇËæ»úµÄ£¬Òò´Ëºó´úµÄ»ùÒòÐͼ°±ÈÀýÊÇAA£ºAa£ºaa=4£º4£º1£¬aa¸öÌåÓ×ÃçÆÚËÀÍö£¬Òò´Ë³ÉÊìÖ²Öê»ùÒòÐͼ°±ÈÀýÊÇAA£ºAa=1£º1£¬aµÄ»ùÒòƵÂÊÊÇ$\frac{1}{4}$£»×Ó¶þ´ú²úÉúµÄÅä×ÓµÄÀàÐͼ°±ÈÀýÊÇA£ºa=3£º1£¬×ÔÓɽ»Åäºó´úµÄ»ùÒòÐͼ°±ÈÀýÊÇAA£ºAa£ºaa=9£º6£º1£¬aaÓ×ÃçÆÚËÀÍö£¬³ÉÊìÖ²Öê»ùÒòÐÍÊÇAA£ºAa=9£º6£¬Òò´ËaµÄ»ùÒòƵÂÊÊÇ$\frac{2}{5}¡Á\frac{1}{2}=\frac{1}{5}$£¬ÒÀ´ËÀàÍÆ£¬¿ÉÖªÖð´ú×ÔÓÉÊڷ۵õ½F_n£¬ÔÚF_n´ú³ÉÊìÖ²ÖêÖÐa»ùÒòƵÂÊÊÇ$\frac{1}{n+2}$£®
¹ÊÑ¡£ºC£®

µãÆÀ ±¾ÌâÖ¼ÔÚ¿¼²éÀí½â»ùÒò·ÖÀ붨ÂɵÄʵÖÊ£¬Çø·Ö×Ô½»Óë×ÔÓɽ»ÅäÏà¹Ø¸ÅÂʵļÆËã¼°»ùÒòƵÂʵļÆËã·½·¨£¬°ÑÎÕ֪ʶµÄÄÚÔÚÁªÏµ£¬²¢Ó¦ÓÃÏà¹Ø֪ʶ½øÐÐÍÆÀí¡¢¼ÆË㣬ѧ»áÓ¦ÓÃÊýѧ·½·¨½â¾öÒÅ´«Ñ§ÎÊÌ⣮