观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1); 1/(x-2)(x-3)=1/(x-3)-1/(x-2);观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1);1/(x-2)(x-3)=1/(x-3)-1/(x-2);1/(x-3)(x-4)=1/(x-4)-1/(x-3);1/(x-4)(x-5)=1/(x-5)-1/(x-4);.(1)你可以归纳出一般结
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![观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1); 1/(x-2)(x-3)=1/(x-3)-1/(x-2);观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1);1/(x-2)(x-3)=1/(x-3)-1/(x-2);1/(x-3)(x-4)=1/(x-4)-1/(x-3);1/(x-4)(x-5)=1/(x-5)-1/(x-4);.(1)你可以归纳出一般结](/uploads/image/z/15128568-0-8.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E5%85%B3%E7%B3%BB%E5%BC%8F%3A1%2F%28x-1%29%28x-2%29%3D1%2F%28x-2%29-1%2F%28x-1%29%3B+1%2F%28x-2%29%28x-3%29%3D1%2F%28x-3%29-1%2F%28x-2%29%3B%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E5%85%B3%E7%B3%BB%E5%BC%8F%3A1%2F%28x-1%29%28x-2%29%3D1%2F%28x-2%29-1%2F%28x-1%29%3B1%2F%28x-2%29%28x-3%29%3D1%2F%28x-3%29-1%2F%28x-2%29%3B1%2F%28x-3%29%28x-4%29%3D1%2F%28x-4%29-1%2F%28x-3%29%3B1%2F%28x-4%29%28x-5%29%3D1%2F%28x-5%29-1%2F%28x-4%29%3B.%281%29%E4%BD%A0%E5%8F%AF%E4%BB%A5%E5%BD%92%E7%BA%B3%E5%87%BA%E4%B8%80%E8%88%AC%E7%BB%93)
观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1); 1/(x-2)(x-3)=1/(x-3)-1/(x-2);观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1);1/(x-2)(x-3)=1/(x-3)-1/(x-2);1/(x-3)(x-4)=1/(x-4)-1/(x-3);1/(x-4)(x-5)=1/(x-5)-1/(x-4);.(1)你可以归纳出一般结
观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1); 1/(x-2)(x-3)=1/(x-3)-1/(x-2);
观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1);
1/(x-2)(x-3)=1/(x-3)-1/(x-2);
1/(x-3)(x-4)=1/(x-4)-1/(x-3);
1/(x-4)(x-5)=1/(x-5)-1/(x-4);
.
(1)你可以归纳出一般结论是____________.
(2)请利用上述结论计算:1/(x+1)+1/(x-1)(x+2)+1/(x-2)(x-3)+...+1/(x-99)(x-100).
观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1); 1/(x-2)(x-3)=1/(x-3)-1/(x-2);观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1);1/(x-2)(x-3)=1/(x-3)-1/(x-2);1/(x-3)(x-4)=1/(x-4)-1/(x-3);1/(x-4)(x-5)=1/(x-5)-1/(x-4);.(1)你可以归纳出一般结
可以归纳出一般的结论是:相邻的两个自然数积的倒数等于这两个自然数的倒数之差!
1/(x-1)(x-2)+1/(x-2)(x-3)+……+1/(x-99)(x-100)
=1/(x-1)-1/(x-2)+1/(x-2)-1/(x-3)+……+1/(x-99)-1/(x-100)
=1/(x-1)-1/(x-100)
=[(x-100)-(x-1)]/[(x-1)(x-100)]
=-99/[(x-1)(x-100)]
观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1); 1/(x-2)(x-3)=1/(x-3)-1/(x-2); 1/(x-3)(x-4)=1/(x-4)-1/(x-3); 1/(x-4)(x-5)=1/(x-5)-1/(x-4); ...
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观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1); 1/(x-2)(x-3)=1/(x-3)-1/(x-2); 1/(x-3)(x-4)=1/(x-4)-1/(x-3); 1/(x-4)(x-5)=1/(x-5)-1/(x-4); ......(1)你可以归纳出一般结论是____________.(2)请利用上述结论计算:1/(x+1)+1/(x-1)(x+2)+1/(x-2)(x-3)+...+1/(x-99)(x-100).
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