Question

一道数学题 急急急急

1/2*(4)+1/4*(6)+1/6*(8)+·······1/2008*(2010)=?
注：1/2*(4） 是指 1/2乘以4 后面也如此 求详解过程 可加分

Answer 1

1/2*(4)=1/2*(1/2-1/4)
1/4*(6)=1/2*(1/4-1/6)
后面以此类推
所以
1/2*(4)+1/4*(6)+1/6*(8)+·······1/2008*(2010)
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+·······1/2008-1/2010)
=1/2*(1/2-1/2010)
=251/1005

Answer 2

=1/2*(2+2)+1/4(4+2)..........1/2008(2008+2)
=1+1+1+1/2+1+1/3+.............1/2008+1/1004
=1004+1005/1004*502
=1004+1005/2

Answer 3

1/2*(4)+1/4*(6)+1/6*(8)+·······1/2008*(2010)
=2/1+3/2+4/3+……+1005/1004
=1004+(1+1/2+1/3+1/4+……+1/1004）

Answer 4

1/2*(4)+1/4*(6)+1/6*(8)+·······1/2008*(2010)
=2/1+3/2+4/3+……+1004/1003
=1003