Question

1/1x4+1/4x7+1/7x10+……+1/2005x2008

Answer 1

1/1*4=1/3*(1/1-1/4)

1/4*7=1/3*(1/4-1/7)

依次可得：

原式=1/3*(1-1/4+1/4-1/7+1/7-1/10……+1/2002-1/2005+1/2005+1/2008)

=1/3*(1-1/2008)

=1/3*2007/2008

=669/2008