(5又11分之6)-3.125-(7又7分之四)-(3又11分之4)+8.125-(3又七分之6)-(2又11分之2)+(6又7分之3)
=[(5又11分之6)-(3又11分之4)-(2又11分之2)]
+[8.125-3.125]
+[(6又7分之3)-(7又7分之四)-(3又七分之6)]
=0+5-5=0
(1/2+1/3+.+1/2007)*(1+1/2+.+1/2006)-(1+1/2+...+1/2007)*(1/2+1/3+.+1/2006)
=[(1/2+1/3+.+1/2007)*(1/2+.+1/2006)+(1/2+1/3+.+1/2007)]-[(1/2+...+1/2007)*(1/2+1/3+.+1/2006)+ (1/2+1/3+.+1/2006)]
=(1/2+1/3+.+1/2007)-(1/2+1/3+.+1/2006)
=1/2007
1*1-2*2+3*3-4*4+.-2004*2004+2005*2005-2006*2006
=(1-2)(1+2)+(3-4)(3+4)+.
+(2003-2004)(2003+2004)+(2005-2006)(2005+2006)
=-(3+7+.+4007+4011)
=-(3+4011)*1003/2
=2013021
(1-1/4)*(1-1/9)*(1-1/16)*.*(1-1/2025)
=[(2^2-1)/2^2]*[(3^2-1)/3^2]*[(4^2-1)/4^2]*.*[(45^2-1)/45^2]
=[(2-1)(2+1)/2^2]*[(3-1)(3+1)/3^2]*[(4-1)(4+1)/4^2]*.
*[(45-1)(45+1)/45^2]
=[(1/2)*(3/2)]*[(2/3)*(4/3)]*[(3/4)*(5/4)]*.
*[(44/45)*(46/45)]
=(1/2)*[(3/2)*(2/3)]*[(4/3)*(3/4)]*[(5/4)*.
*(44/45)]*(46/45)
=(1/2)*(46/45)
=23/45
由于1+2+3+4+……+44=(1+44)*44/2=9901000
故用1+2+3+.+到某数的某数为44
重复的那一个数字为：1000-990=10