Question

计算下列问题

Answer 1

原式=（1-1/3+1/3-1/5+1/5-1/7+…+1/1997-1/1999）/2
=999/1999

Answer 2

1/(1*3)+1/(3*5)+1/(5*7)+……+1/(1007*1999)
=1/2*[1-1/3+1/3-1/5+1/5-1/7+……+1/1997-1/1999]
=1/2*[1-1/1999]
=1/2*1998/1999
=999/1999 .