Question

初一数学探究题

1/2×4=1/4×1/1×2
1/4×6=1/4×1/2×3
1/6×8=1/4×1/3×4
......
1/2010×2012=1/4×6+1/4×6+1/6×8+......+1/2010×2012

注：如1/2×4师2×4分之一，不是1/2×4，全部分数都是这样，请大家注意
用简便计算

Answer 1

解：1/(2*4)+1/(4*6)+1/(6*8)+......+1/(200*2012)
=1/4(1/2+1/6+...+1/(1005*1006))
可以看到如下规律：
1/2=1-1/2
1/6=1/2-1/3
......
1/(1005*1006)=1/1005-1/1006
∴等式=1/4(1-1/2+1/2-1/3+1/3......-1/1006)
=1/4(1-1/1006)
=1/4*1005/1006
=1005/4024

Answer 2

1/2×4=1/4×1/1×2=1/4(1-1/2)
1/4×6=1/4×1/2×3=1/4(1/2-1/3)
1/6×8=1/4×1/3×4=1/4(1/3-1/4)
。。。
1/2010×2012=1/4×1/1005×1006=1/4(1/1005-1/1006)
所以1/2×4+1/4×6+1/6×8+...+1/2010×2012
=1/4(1-1/2)+1/4(1/2-1/3)+1/4(1/3-1/4)+...+1/4(1/1005-1/1006)
=1/4(1-1/2+1/2-1/3+1/3-1/4+...+1/1005-1/1006)
=1/4(1-1/1006)
=1/4*1005/1006
=1005/4024

Answer 3

上面