1/2x4+1/4x6+1/6x8+...+1/2006x2008=______要讲解,一步一步的讲解,

1/2x4+1/4x6+1/6x8+...+1/2006x2008=______要讲解,一步一步的讲解,
1/2x4+1/4x6+1/6x8+...+1/2006x2008=______要讲解,一步一步的讲解,

1/2x4+1/4x6+1/6x8+...+1/2006x2008=______要讲解,一步一步的讲解,
1/2x4+1/4x6+1/6x8+...+1/2006x2008
=（1/2-1/4+1/4-1/6+1/6-1/8+……+1/2006-1/2008）÷2
=（1/2-1/2008）÷2
=1003/2008÷2
=1003/4016

1/2x4+1/4x6+1/6x8+...+1/2006x2008
=1/2*1/2(1/1*2+1/2*3+1/3*4+...+1/1003*1004)
=1/4(1-1/2+1/2-1/3+1/3-1/4...+1/1003-1/1004)
=1/4(1-1/1004)
=1003/4016