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)直接写出下列各式的计算结果1/1*2+1/2*3
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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)直接写出下列各式的计算结果1/1*2+1/2*3](/uploads/image/z/8818661-29-1.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.%EF%BC%881%EF%BC%89%E7%8C%9C%E6%83%B3%E5%B9%B6%E5%86%99%E5%87%BA%EF%BC%9A1%2Fn%28n%2B1%29%3D______%3B%282%29%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%9C1%2F1%2A2%2B1%2F2%2A3)
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)直接写出下列各式的计算结果1/1*2+1/2*3
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)直接写出下列各式的计算结果
1/1*2+1/2*3+1/3*4+...+1/99*100=_________;
(3)计算:1/1*2+1/2*3+1/3*4...+1/n(n+1).
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)直接写出下列各式的计算结果1/1*2+1/2*3
裂项法:
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)=1/n-1/(n+1);
(2)直接写出下列各式的计算结果
1/1*2+1/2*3+1/3*4+...+1/99*100=1-1/100=99/100;
(3)计算:
1/1*2+1/2*3+1/3*4...+1/n(n+1)
=1-1/2+1/3-1/3+1/3-1/4+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
1/n-1/(n+1)
1-1/100=99/100
1-1/(n+1)=n/(n+1)
(1)1/n(n+1)=1/n-1/(n+1)
(2)99/100
(3)原式=1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)=1-1/n+1)=n/(n+1)