ÌâÄ¿ÄÚÈÝ

1£®É躯Êýf£¨n£©=$\left\{\begin{array}{l}{n£¬nÎªÆæÊý}\\{f£¨\frac{n}{2}£©£¬nΪżÊý}\end{array}\right.$£¬an=f£¨1£©+f£¨2£©+f£¨3£©+¡­+f£¨2n£©£¬
£¨1£©Çóa1£¬a2£¬a3µÄÖµ
£¨2£©Éèbn=an+1-an£¬Ð´³öbnÓëbn+1µÄµÝÍÆ¹ØÏµ£¬²¢Çó{bn}µÄͨÏʽ£®
£¨3£©ÉèÊýÁÐ{cn}µÄͨÏʽΪcn=log2£¨3an-2£©-10£¬n¡ÊN*£¬ÊýÁÐ{cn}µÄǰnÏîºÍΪSn£¬
ÎÊ1000ÊÇ·ñΪÊýÁÐ{cn•Sn}ÖеÄÏÈôÊÇ£¬Çó³öÏàÓ¦µÄÏîÊý£¬Èô²»ÊÇ£¬Çë˵Ã÷ÀíÓÉ£®

·ÖÎö £¨1£©Óɺ¯Êýf£¨n£©£¬½áºÏan£¬¿ÉµÃa1£¬a2£¬a3£»
£¨2£©ÓÉÌâÒ⣬µÃan+1=f£¨1£©+f£¨2£©+f£¨3£©+¡­+f£¨2n£©+f£¨2n+1£©+¡­+f£¨2n+1£©£¬×÷²î£¬µÃan+1-an£¬Óɺ¯Êý½âÎöʽ½áºÏµÈ²îÊýÁеÄÇóºÍ¹«Ê½¼ÆËã¿ÉÇóµÃ½á¹û£»
£¨3£©ÓÉan=a1+£¨a2-a1£©+£¨a3-a2£©+¡­+£¨an-an-1£©£¬ÔËÓõȱÈÊýÁеÄÇóºÍ¹«Ê½¿ÉµÃan£¬cn£¬ÔÙÓɵȲîÊýÁеÄÇóºÍ¹«Ê½£¬ÔÙÓÉcn•Sn£¬¼´¿ÉÅжÏ1000ÊÇ·ñÔÚÆäÖУ®

½â´ð ½â£º£¨1£©Óɺ¯Êýf£¨n£©=$\left\{\begin{array}{l}{n£¬nÎªÆæÊý}\\{f£¨\frac{n}{2}£©£¬nΪżÊý}\end{array}\right.$£¬
an=f£¨1£©+f£¨2£©+f£¨3£©+¡­+f£¨2n£©£¬µÃ
a1=f£¨1£©+f£¨2£©=1+f£¨1£©=2£»
a2=f£¨1£©+f£¨2£©+f£¨3£©+f£¨4£©=1+1+3+f£¨2£©=5+1=6£»
a3=f£¨1£©+f£¨2£©+f£¨3£©+f£¨4£©+f£¨5£©+f£¨6£©+f£¨7£©+f£¨8£©=1+1+3+1+5+3+7+1=22£»
£¨2£©ÓÉan=f£¨1£©+f£¨2£©+f£¨3£©+¡­+f£¨2n£©£¬
¿ÉµÃan+1=f£¨1£©+f£¨2£©+f£¨3£©+¡­+f£¨2n£©+f£¨2n+1£©+¡­+f£¨2n+1£©£¬
ÔòÓÐbn=an+1-an=f£¨2n+1£©+¡­+f£¨2n+1£©
=£¨2n+1£©+£¨2n-1+1£©+£¨2n+3£©+£¨2n-2+1£©+£¨2n+5£©+£¨2n-1+3£©+¡­+1
=1+3+5+¡­+£¨2n+1£©+¡­+£¨2n+1-1£©=$\frac{1}{2}$£¨1+2n+1-1£©•2n
=4n£®
¼´ÓÐbn+1=4bn£¬ÇÒbn=4n£»
£¨3£©ÓÉan=a1+£¨a2-a1£©+£¨a3-a2£©+¡­+£¨an-an-1£©
=2+4+16+..+4n-1=2+$\frac{4£¨1-{4}^{n-1}£©}{1-4}$=$\frac{{4}^{n}+2}{3}$£¬
¼´ÓÐcn=log2£¨3an-2£©-10=2n-10£¬
Sn=$\frac{1}{2}$n£¨c1+cn£©=$\frac{1}{2}$n£¨2n-18£©=n£¨n-9£©£¬
¼´ÓÐcn•Sn=2n£¨n-5£©£¨n-9£©£¬
µ±n¡Ü13ʱ£¬cn•Sn¡Üc13•S13=832£¼1000£¬
µ±n¡Ý13ʱ£¬cn•Sn¡Ýc14•S14=1260£¾1000£¬
¹Ê1000²»ÊÇ{cn•Sn}ÖеÄÏ

µãÆÀ ±¾Ì⿼²éÁ˷ֶκ¯ÊýÓëÊýÁÐͨÏʽµÄ×ÛºÏÓ¦Óã¬Ö÷Òª¿¼²é·Ö¶Îº¯ÊýµÄÒâÒåºÍµÈ²îÊýÁеÄÇóºÍ¹«Ê½£¬ÒÔ¼°ÀÛ¼Ó·¨ÇóÊýÁеÄͨÏ¿¼²éÔËËãÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿

Î¥·¨ºÍ²»Á¼ÐÅÏ¢¾Ù±¨µç»°£º027-86699610 ¾Ù±¨ÓÊÏ䣺58377363@163.com

¾«Ó¢¼Ò½ÌÍø