Question

计算:(1/2+1/3+1/4+...+1/2008)(1+1/2+1/3+1/4+...1/2007)-(1+1/2+1/3+1/4...+1/2008)(1/2+1/3+..+1/2007)

求计算过程

Answer 1

设a=1/2+1/3+..+1/2007，b=1+1/2+1/3+1/4+...1/2007
原式=（a+1/2008）*b-（b+1/2008）*a
=ab+b*1/2008-ab-a*1/2008
=（b-a）*1/2008
=1*1/2008
=1/2008

Answer 2

原式=(1/2+1/3+1/4+...+1/2008)+(1/2+1/3+1/4+...+1/2008)(1/2+1/3+1/4+...1/2007）-(1/2+1/3+..+1/2007)-（1/2+1/3+1/4...+1/2008）(1/2+1/3+..+1/2007)
=1/2008

Answer 3

(1/2+1/3+...1/2008)(1+1/2+1/3+...1/2007)-(1/2+1/3+...1/2008)(1/2+1/3+...1/2007)-(1/2+1/3+...1/2007)=(1/2+1/3+...1/2008)-(1/2+1/3+...1/2007)=1/2008