对于任意实数a b 定义新运算*如下：a*b=a-b/2ab,试求4*2+6*4+~+2014*2012的值

(n+2)*n=(n+2-n)/2n(n+2)
=1/2*2/n(n+2)
=1/2*[1/n-1/(n+2)]
所以原式=1/2(1/2-1/4+1/4-1/6+……+1/2012-1/2014)
=1/2(1/2-1/2014)
=503/2014