1/1*2+1/2*3+1/3*4+…+1/1001*1002

Question

1/1*2+1/2*3+1/3*4+…+1/1001*1002

Answer 1

答：
考查分数的裂项知识
1/1*2+1/2*3+1/3*4+…+1/1001*1002
=1-1/2+1/2-1/3+1/3-1/4+...+1/1001-1/1002
=1-1/1002 （中间全部正负项抵消了）
=1001/1002