1/1*2+1/2*3+1/3*4+······+

1/1*2+1/2*3+1/3*4+······+1/2007*2008等于多少（加解题方法）

1个回答

1/(1×2)+1/(2×3)+1/(3×4)+…1/(2005×2006)+1/(2006×2007)+1/(2007×2008)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+…+(1/2007-1/2008)
=1-1/2+1/2-1/3+1/3-1/4+…+1/2007-1/2008
=1-1/2008
=2007/2008