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化简:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+1998)(x+1999) 是多少
这是一道8年下的数学题
人气:466 ℃ 时间:2020-02-03 15:34:08
解答
裂项相消:
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)
=1998/x(x+1999)
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