计算2004/1949*1950+2004/1950*1951+2004/1951*1952+.+2004/2003*2

根据1/N(N+1)=1/N-1/(N+1) 原式=2004X(1/1949-1/1950+1/1950-1/1951+.+1/2003-1/2004) =2004X(1/1949-1/2004) =2004/1949-1 =55/1949