Question

初中数学计算题

对于任意非零实数a、b，定义运算a*b=a-b/ab，则2*1+3*2+4*3+···+2009*2008=？

Answer 1

2*1+3*2+4*3+···+2009*2008
=(2-1)/2+(3-2)/6+(4-3)/12.......(2009-2008)/2009乘2008
=1/2+1/6+1/12+.......1/2009乘2008
=(1-1/2)+(1/2-1/3)+(1/3-1/4).......+(1/2008-1/2009)
=1-1/2+1/2-1/3+1/3-1/4.......+1/2008-1/2009
=1-1/2009
=2008/2009

Answer 2

按定义的运算a*b=a-b/ab，则
2*1+3*2+4*3+···+2009*2008
=(2-1)/2+(3-2)/6+(4-3)/12+...+(2009-2008)/(2009*2008)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2008-1/2009
=2008/2009

Answer 3

=（1-1/2）+（1/2-1/3)+。。。+（1/2008-1/2009)
=2008/2009