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求救，以下初中数学题何解？1/(1x3)+1/(2x4)+1/(

2007-10-31 23:07:31t***
1/(1x3)+1/(2x4)+1/(3x5)+...+1/(1998x2000)=?求救，以下初中数学题何解？1/(1x3)+1/(2x4)+1/(3x5)+...+1/(1998x2000)=?：1/(1x3)+1/(2x4)+1/(3x5)?

最佳回答

  • 1/(1x3)+1/(2x4)+1/(3x5)+...+1/(1998x2000) = [1/(1x3)+1/(3x5)+...+1/(1997x1999)] + + (1/4)*[1/(1x2)+1/(2x3)+...+1/(999x1000)] = (1/2)*[(1/1-1/3)+(1/3-1/5)+...+(1/1997-1/1999)]+ + (1/4)*[(1/1-1/2)+(1/2-1/3)+...+(1/999-1/1000)] = (1/2)*[1 -1/1999] +(1/4)*[1 -1/1000] = 999/1999 +999/4000 = ...
    2007-10-31 23:41:27
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