简便计算2001/(2001+2002/2003)+1/2003

2001=2002-1,2003=2002+1 2001/(2001+2002/2003)+1/2003=（2002-1）/[(2002-1)+2002/(2002+1)]+1/(2002+1)=(2002-1)/{[(2002-1)(2002+1)+2002]/(2002+1)}+1/(2002+1)=(2002-1)（2002+1）/[(2002-1)(2002+1)+2002]+1/(2002+1)为了看起来方便 把2002用a代替 =(a²-1)/(a²-1+a)+1/(a+1) 通分=[(a²-1)(a+1)+(a²+a-1)]/[(a²+a-1)(a+1)]=(aaa-a+a²-1+a²+a-1)/(aaa+a²-a+a²+a-1)=(aaa+2a²-2)/(aaa+2a²-1)比较分子 分母相差1 并且分母分子都很大所以此题约等于1