(1996+95*1997)/(1996*1997-1)+(1997+1996*1998)/(1997*1998-1)+(1998+1997*1999)/(1998*1999-1)

题目

(1996+95*1997)/(1996*1997-1)+(1997+1996*1998)/(1997*1998-1)+(1998+1997*1999)/(1998*1999-1)

答案

(1996+1995*1997)/(1996*1997-1)+(1997+1996*1998)/(1997*1998-1)+(1998+1997*1999)/(1998*1999-1)
令a=1996
原式
=[a+(a-1)(a+1)]/[a(a+1)-1]+[(a+1)+a(a+2)]/[(a+1)(a+2)-1]+[(a+2)+(a+1)(a+3)]/[(a+2)(a+3)-1]
=(a+a²-1)/(a²+a-1)+(a²+3a+1)/(a²+3a+1)+(a²+5a+5)/(a²+5a+5)
=1+1+1
=3