计算1/[x(x+1)]+1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+……+1/[(x+1998)(x+1999)]1/x-1/(x+1999)怎么两个除号?懂的人用分数告诉我 1————X用这样的形式.
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![计算1/[x(x+1)]+1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+……+1/[(x+1998)(x+1999)]1/x-1/(x+1999)怎么两个除号?懂的人用分数告诉我 1————X用这样的形式.](/uploads/image/z/1630973-29-3.jpg?t=%E8%AE%A1%E7%AE%971%2F%5Bx%28x%2B1%29%5D%2B1%2F%5B%28x%2B1%29%28x%2B2%29%5D%2B1%2F%5B%28x%2B2%29%28x%2B3%29%5D%2B%E2%80%A6%E2%80%A6%2B1%2F%5B%28x%2B1998%29%28x%2B1999%29%5D1%2Fx-1%2F%28x%2B1999%29%E6%80%8E%E4%B9%88%E4%B8%A4%E4%B8%AA%E9%99%A4%E5%8F%B7%3F%E6%87%82%E7%9A%84%E4%BA%BA%E7%94%A8%E5%88%86%E6%95%B0%E5%91%8A%E8%AF%89%E6%88%91+1%E2%80%94%E2%80%94%E2%80%94%E2%80%94X%E7%94%A8%E8%BF%99%E6%A0%B7%E7%9A%84%E5%BD%A2%E5%BC%8F.)
计算1/[x(x+1)]+1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+……+1/[(x+1998)(x+1999)]1/x-1/(x+1999)怎么两个除号?懂的人用分数告诉我 1————X用这样的形式.
计算1/[x(x+1)]+1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+……+1/[(x+1998)(x+1999)]
1/x-1/(x+1999)
怎么两个除号?懂的人用分数告诉我
1
————
X
用这样的形式.
计算1/[x(x+1)]+1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+……+1/[(x+1998)(x+1999)]1/x-1/(x+1999)怎么两个除号?懂的人用分数告诉我 1————X用这样的形式.
因为:
1/(1*2)=1/2=1-1/2
1/(3*4)=1/12=1/3-1/4
.
1/x(x+1)=1/x-1/(x+1)
所以,
1/[x(x+1)]+1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+……+1/[(x+1998)(x+1999)]
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+.+1/(x+1998)-1/(x+1999)
=1/x-1/(x+1999)
=1999/[x(x+1999)]
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