计算:(1/2+1/3+1/4+...+1/2006)*(1+1/2+1/3+1/4+...+1/2006)

问题描述:

计算:(1/2+1/3+1/4+...+1/2006)*(1+1/2+1/3+1/4+...+1/2006)
计算:(1/2+1/3+1/4+...+1/2006)×(1+1/2+1/3+1/4+...+1/2006)-(1+1/2+1/3+1/4+...+1/2007)×(1/2+1/3+1/4+...+1/2006
写错。是:计算:(1/2+1/3+1/4+...+1/2007)×(1+1/2+1/3+1/4+...+1/2006)-(1+1/2+1/3+1/4+...+1/2007)×(1/2+1/3+1/4+...+1/2006

(1/2+1/3+1/4+...+1/2006)×(1+1/2+1/3+1/4+...+1/2006)-(1+1/2+1/3+1/4+...+1/2007)×(1/2+1/3+1/4...+1/2006 )
=(1/2+1/3+1/4+...+1/2006)×(1+1/2+1/3+1/4+...+1/2006)-(1+1/2+1/3+1/4+...+1/2006+1/2007)×(1/2+1/3+1/4+...+1/2006 )
=(1/2+1/3+1/4+...+1/2006)×(1+1/2+1/3+1/4+...+1/2006)-(1+1/2+1/3+1/4+...+1/2006)×(1/2+1/3+1/4+...+1/2006 )-1/2007*(1/2+1/3+1/4+...+1/2006 )
=-1/2007*(1/2+1/3+1/4+...+1/2006 )上面写错了。。。是: 计算:(1/2+1/3+1/4+...+1/2007)×(1+1/2+1/3+1/4+...+1/2006)-(1+1/2+1/3+1/4+...+1/2007)×(1/2+1/3+1/4+...+1/2006 )(1/2+1/3+1/4+...+1/2007)×(1+1/2+1/3+1/4+...+1/2006)-(1+1/2+1/3+1/4+...+1/2007)×(1/2+1/3+1/4+...+1/2006 )

=(1/2+1/3+1/4+...+1/2006+1/2007)×(1+1/2+1/3+1/4+...+1/2006)-(1+1/2+1/3+1/4+...+1/2006+1/2007)×(1/2+1/3+1/4+...+1/2006 )

=(1/2+1/3+1/4+...+1/2006)×(1+1/2+1/3+1/4+...+1/2006)+1/2007(1+1/2+1/3+1/4+...+1/2006)
-(1+1/2+1/3+1/4+...+1/2006)×(1/2+1/3+1/4+...+1/2006 -1/2007(1+1/2+1/3+1/4+...+1/2006)+1/2007
=1/2007