Question

对于任意非零实数a、b定义运算如下a*b=a-b/ab,求2*1+3*2+4*3+……+2002*2001的值

初二下学期数学

Answer 1

2*1+3*2+4*3+……+2002*2001
=(2-1)/1x2+(3-2)/2x3+(4-3)/4x3+········+(2002-2001)/2001x2002
=1/1-1/2+1/2-1/3+1/3-1/4+···········+1/2001-1/2002
=1-1/2002
=2001/2002

Answer 2

是a*b=(a-b)/ab吧，如果是的话，a*b=(1/b)-(1/a)，
则，所求式=1/1-1/2+1/2-1/3+......+1/2001-1/2002=2001/2002