Question

1/1x2+1/2x3+1/3x4+1/4x5+.+1/2007x2008=多少 怎么计算

Answer 1

1/1x2+1/2x3+1/3x4+1/4x5+.+1/2007x2008(任何一项积分母分之一可化成两个互减单项式形式,没什么公式,只是个特例)

=(1/1-1/2)+ (1/2-1/3)+(1/3-1/4)+(1/4-1/5)+,+(1/2007-1/2008)

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/2007-1/2008

=1-1/2008(中间项全部抵消,只剩下两端的项)

=2007/2008