有關求級數和的題目(分數型)

P=(1/1*2) (1/3*4) (1/5*6) ...... (1/2003*2004)Q=(1/1003*2004) (1/1004*2003) ...... (1/2004*1003)求P/Q=?
P=(1/1*2) (1/3*4) (1/5*6) ...... (1/ 2003*2004) =[(1/1)-(1/2)] [(1/3)-(1/4)] [(1/5)-(1/6)] ....[(1/2003)-(1/2004)]=[(1/ 1) (1/3) (1/5) ... (1/2003) ]-[(1/2) (1/4) (1/6) ... (1/2004)] =[(1/1) (1/2) (1/3) (1/4) ... (1/2004)] -2*[(1/2) (1/4) (1/6) ... (1/2004)]= [(1/1) (1/2) (1/3) (1/4) ... (1/2004)]-[(1/1) (1/2) (1/3) .. (1/1002)]= (1/1003) (1/1004) (1/1005) .... (1/2004)Q=(1/1003*2004) (1/1004*2003) ...... (1/2004*1003) = 2*[(1/1003*2004) (1/1004*2003) (1/1005*2002) .... (1/1503*1504)](1/1003) (1/2004)=3007/1003*2004----