对于非零实数a b一种新定义算法“*”如下:a*b=a-b/ab 求:2*1+3*2+4*3+.+2009*2008如题

问题描述:

对于非零实数a b一种新定义算法“*”如下:a*b=a-b/ab 求:2*1+3*2+4*3+.+2009*2008
如题

2*1+3*2+4*3+.....+2009*2008
=1/(2*1)+1/(3*2)+1/(4*3)+......+1/(2009*2008)
=1-1/2+1/2-1/3+1/3-1/4+.....+1/2008-1/2009
=1-1/2009=2008/2009

2*1+3*2+4*3+……+2009*2008
=1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2008×2009)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2008-1/2009
=1- 1/2009
=2008/2009