Question

1乘2分之1加2乘3分之1加3乘4分之1加……加2007乘2008分之1

Answer 1

1/(1*2)+1/(2*3)+1/(3*4)+.1/(2007*2008)=

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

1-1/2008=

2007/2008