一道八年级下册分式探究题观察下列等式 1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4将以上三个等式两边分别相加得1/1*2+1/2*3+1/3*4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4探究并计算1/2*4+1/4*6+1/6*8+.+1/2006*2008
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![一道八年级下册分式探究题观察下列等式 1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4将以上三个等式两边分别相加得1/1*2+1/2*3+1/3*4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4探究并计算1/2*4+1/4*6+1/6*8+.+1/2006*2008](/uploads/image/z/6903019-19-9.jpg?t=%E4%B8%80%E9%81%93%E5%85%AB%E5%B9%B4%E7%BA%A7%E4%B8%8B%E5%86%8C%E5%88%86%E5%BC%8F%E6%8E%A2%E7%A9%B6%E9%A2%98%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F+1%2F1%2A2%3D1-1%2F2%2C1%2F2%2A3%3D1%2F2-1%2F3%2C1%2F3%2A4%3D1%2F3-1%2F4%E5%B0%86%E4%BB%A5%E4%B8%8A%E4%B8%89%E4%B8%AA%E7%AD%89%E5%BC%8F%E4%B8%A4%E8%BE%B9%E5%88%86%E5%88%AB%E7%9B%B8%E5%8A%A0%E5%BE%971%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%3D1-1%2F2%2B1%2F2-1%2F3%2B1%2F3-1%2F4%3D1-1%2F4%3D3%2F4%E6%8E%A2%E7%A9%B6%E5%B9%B6%E8%AE%A1%E7%AE%971%2F2%2A4%2B1%2F4%2A6%2B1%2F6%2A8%2B.%2B1%2F2006%2A2008)
一道八年级下册分式探究题观察下列等式 1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4将以上三个等式两边分别相加得1/1*2+1/2*3+1/3*4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4探究并计算1/2*4+1/4*6+1/6*8+.+1/2006*2008
一道八年级下册分式探究题
观察下列等式 1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4
将以上三个等式两边分别相加得1/1*2+1/2*3+1/3*4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4
探究并计算1/2*4+1/4*6+1/6*8+.+1/2006*2008
一道八年级下册分式探究题观察下列等式 1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4将以上三个等式两边分别相加得1/1*2+1/2*3+1/3*4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4探究并计算1/2*4+1/4*6+1/6*8+.+1/2006*2008
1/2*4+1/4*6+1/6*8+····+1/2006*2008
=(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2006-1/2008)/2
=(1/2-1/2008)/2
=1003/4016
原式=1/2(1/2-1/4+1/4-1/6+....-1/2008)
=1/2*(1/2-1/2008)
=1003/4016
1/2*4+1/4*6+1/6*8+。。。。。。+1/2006*2008
=(1/4)(1/1*2+1/2*3+1/3*4...+1/1003*1004
=(1/4)(1-1/2+1/2-1/3+1/3...1/1003-1/1004)
=(1/4)(1-1/1004)
=(1/4)*1003/1004
=1003/4016