Question

计算1乘4分之1加4乘7分之1加7乘10分之1加.加2005乘2008分之1的和

Answer 1

1/(1x4)+1/(4x7)+1/(7x10)+...+1/(2005x2008)

=1/3*(1/1-1/4)+1/3*(1/4-1/7)+1/3*(1/7-1/10)+...+1/3*(1/2005-1/2008)

=1/3*(1/1-1/4+1/4-1/7+1/7-1/10+...+1/2005-1/2008)

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

=1/3*2007/2008=669/2008