ÌâÄ¿ÄÚÈÝ

ÈçͼËùʾ£¬ÔÚxÖáµÄÕý°ëÖáÉÏÒÀ´Î½ØÈ¡OA1=A1A2=A2A3=A3A4¡­=A2n-1A2n=1£¬¹ýA1¡¢A3¡¢A5¡­A2n-1·Ö±ð×÷xÖáµÄ´¹ÏßÓë·´±ÈÀýº¯Êýy=
2
x
µÄͼÏó½»ÓÚµãB1¡¢B3¡¢B5¡­B2n-1£¬Óë·´±ÈÀýº¯Êýy=
4
x
µÄͼÏó½»ÓÚµãC1¡¢C3¡¢C5¡¢¡­C2n-1£¬²¢Éè¡÷OB1C1Óë¡÷B1C1A2ºÏ²¢³ÉµÄËıßÐεÄÃæ»ýΪS1£¬¡÷A2B2C3Óë¡÷B2C3A4ºÏ²¢³ÉµÄËıßÐεÄÃæ»ýΪS2¡­£¬ÒÔ´ËÀàÍÆ£¬¡÷A2n-2BnCnÓë¡÷BnCnA2nºÏ²¢³ÉµÄËıßÐεÄÃæ»ýΪSn£¬ÔòS1=______£»
1
s1
+
1
s2
+
1
s3
+¡­+
1
sn
=______£®£¨nΪÕýÕûÊý£©£®
¡ßÔÚxÖáµÄÕý°ëÖáÉÏÒÀ´Î½ØÈ¡OA1=A1A2=A2A3=A3A4¡­=A2n-1A2n=1£¬¹ýA1¡¢A3¡¢A5¡­A2n-1·Ö±ð×÷xÖáµÄ´¹ÏßÓë·´±ÈÀýº¯Êýy=
2
x
µÄͼÏó½»ÓÚµãB1¡¢B3¡¢B5¡­B2n-1£¬Óë·´±ÈÀýº¯Êýy=
4
x
µÄͼÏó½»ÓÚµãC1¡¢C3¡¢C5¡¢¡­C2n-1£¬
¡àOA1•B1A1=2£¬OA1•C1A1=4£¬
¡à¡÷OB1C1Óë¡÷B1C1A2ºÏ²¢³ÉµÄËıßÐεÄÃæ»ýΪS1=
1
2
¡Á2OA1•C1A1-
1
2
¡Á2OA1•B1A1=2£¬
ͬÀí¿ÉµÃ³ö£ºOA3•C3A3=4£¬OA3•B3A3=2£¬
¡àC3A3=
4
3
£¬B3A3=
2
3
£¬
¡à¡÷A2B2C3Óë¡÷B2C3A4ºÏ²¢³ÉµÄËıßÐεÄÃæ»ýΪS2=
1
2
¡Á2A2A3•C3A3-
1
2
¡Á2A2A3•B3A3=
2
3
£¬
¿ÉµÃ³ö£ºS3=
2
5
£¬
¡àSn=
2
2n-1
£¬
¡à
1
s1
+
1
s2
+
1
s3
+¡­+
1
sn
=
1
2
+
3
2
+
5
2
+¡­+
2n-1
2
=
1+3+5+¡­+(2n-1)
2
=
n2
2
£¨nΪÕýÕûÊý£©£®
¹Ê´ð°¸Îª£º2£¬
n2
2
£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿

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

¾«Ó¢¼Ò½ÌÍø