观察下列等式:1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4,将以上三个等式两边相加得:1/1x2+1/2x3+1/3x4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4(1)猜想并写出1/n(n+1)=(2)直接写出下列各式的计算结果:1/1x2+1/2x3+1/3x4
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![观察下列等式:1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4,将以上三个等式两边相加得:1/1x2+1/2x3+1/3x4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4(1)猜想并写出1/n(n+1)=(2)直接写出下列各式的计算结果:1/1x2+1/2x3+1/3x4](/uploads/image/z/1765082-2-2.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F%EF%BC%9A1%2F1x2%3D1-1%2F2%2C1%2F2x3%3D1%2F2-1%2F3%2C1%2F3x4%3D1%2F3-1%2F4%2C%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%E7%9B%B8%E5%8A%A0%E5%BE%97%EF%BC%9A1%2F1x2%2B1%2F2x3%2B1%2F3x4%3D1-1%2F2%2B1%2F2-1%2F3%2B1%2F3-1%2F4%3D1-1%2F4%3D3%2F4%EF%BC%881%EF%BC%89%E7%8C%9C%E6%83%B3%E5%B9%B6%E5%86%99%E5%87%BA1%2Fn%EF%BC%88n%2B1%EF%BC%89%3D%EF%BC%882%EF%BC%89%E7%9B%B4%E6%8E%A5%E5%86%99%E5%87%BA%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E8%AE%A1%E7%AE%97%E7%BB%93%E6%9E%9C%EF%BC%9A1%2F1x2%2B1%2F2x3%2B1%2F3x4)
观察下列等式:1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4,将以上三个等式两边相加得:1/1x2+1/2x3+1/3x4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4(1)猜想并写出1/n(n+1)=(2)直接写出下列各式的计算结果:1/1x2+1/2x3+1/3x4
观察下列等式:1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4,将以上三个等式两边相加得:
1/1x2+1/2x3+1/3x4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4
(1)猜想并写出1/n(n+1)=
(2)直接写出下列各式的计算结果:1/1x2+1/2x3+1/3x4+...+1/2011x2012=
(3)探究并计算:1/1x2+1/2x3+1/3x4+...+1/n(n+1)=
观察下列等式:1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4,将以上三个等式两边相加得:1/1x2+1/2x3+1/3x4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4(1)猜想并写出1/n(n+1)=(2)直接写出下列各式的计算结果:1/1x2+1/2x3+1/3x4
1/n(n+1)=1/n-1/(n+1)
1/1x2+1/2x3+1/3x4+...+1/2011x2012
=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012
=1-1/2012
=2011/2012
1/1x2+1/2x3+1/3x4+...+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
1/n(n+1)=1/n-1/(n+1)
1/1x2+1/2x3+1/3x4+...+1/2011x2012
=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012
=1-1/2012
=2011/2012
1/1x2+1/2x3+1/3x4+...+1/n(n+1)
=1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)