Question

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

Answer 1

a*b=（a-b）/ab＝(1/b)-(1/a)

2*1+3*2+4*3+……+2002*2001

=( 1-1/2)+(1/2-1/3)+1/3-1/4)+.+(1/2001-1/2002)

=1-(1/2002)

=2001/2002