Question

一列数：1/2,1/6,1/12,1/20,1/30,1/42.用简便算法计算这列数前2005项的和

Answer 1

对任意的正整数n都有1/n(n+1)=1/n-1/(n+1)

1/2+1/6+……+1/(2005*2006)

=(1-1/2)+(1/2-1/3)+……+(1/2005-1/2006)

=1-1/2006

=2005/2006