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.(1)猜想并写出:1/n(n+1)=() (2)1/1*2+1/2*3+1/3*4+...+1/2013*2014
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![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.(1)猜想并写出:1/n(n+1)=() (2)1/1*2+1/2*3+1/3*4+...+1/2013*2014](/uploads/image/z/8818660-28-0.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F%EF%BC%9A1%2F1%2A2%3D1-1%2F2%2C1%2F2%2A3%3D1%2F2-1%2F3%2C1%2F3%2A4%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%E5%88%86%E5%88%AB%E7%9B%B8%E5%8A%A0%E5%BE%97%EF%BC%9A1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%3D1-1%2F2%2B1%2F2-1%2F3%2B1%2F3-1%2F4%3D1-1%2F4%3D3%2F4.%281%29%E7%8C%9C%E6%83%B3%E5%B9%B6%E5%86%99%E5%87%BA%EF%BC%9A1%2Fn%28n%2B1%29%3D%EF%BC%88%EF%BC%89+%EF%BC%882%EF%BC%891%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B...%2B1%2F2013%2A2014)
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.(1)猜想并写出:1/n(n+1)=() (2)1/1*2+1/2*3+1/3*4+...+1/2013*2014
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.
(1)猜想并写出:1/n(n+1)=() (2)1/1*2+1/2*3+1/3*4+...+1/2013*2014
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.(1)猜想并写出:1/n(n+1)=() (2)1/1*2+1/2*3+1/3*4+...+1/2013*2014
1/n-1/(n+1)
1-1/2014=2013/2014