Question

1除以2乘4加上1除以4乘6加到1除以2006乘2008

Answer 1

1除以2乘4加上1除以4乘6加到1除以2006乘2008
=1/2×(1/2-1/4)+1/2×(1/4-1/6)+……+1/2×(1/2006-1/2008)
=1/2×(1/2-1/4+1/4-1/6+……+1/2006-1/2008)
=1/2×(1/2-1/2008)
=1/2×(1004/2008-1/2008)
=1/2×1003/2008
=1003/4016

Answer 2

1÷2×4+1÷4×6+1÷2006×2008
=2+（3/2）+（2008/2006）
=2+（3/2）+（1004/1003）
=9029/2006.

追问

你没看见这局话中的“到”吗？
1除以2乘4加上1除以4乘6加“到”1除以2006乘2008

追答

知道了。用裂项法：
由1/2×4+1/4×6+1/6×8+。。。+1/2006×2008
=（1/2）（2/2×4+2/4×6+2/6×8+。。。+2/2006×2008）
=（1/2）[（1/2-1/4）+（1/4-1/6）+（1/6-1/8）+。。。+（1/2006-1/2008)]
=(1/2)(1/2-1/2008)
=1003/4016.

Answer 3

=1/2×(1/2-1/4)+1/2×(1/4-1/6)+……+1/2×(1/2006-1/2008)
=1/2×(1/2-1/4+1/4-1/6+……+1/2006-1/2008)
=1/2×(1/2-1/2008)
=1/2×(1004/2008-1/2008)
=1/2×1003/2008
=1003/4016