1/x(x+1) + 1/(x+1)(x+2) + 1/(x+2)(x+3)+…… + 1/(x+1

发布时间：2021-03-05 18:42:51

1/x(x+1) + 1/(x+1)(x+2) + 1/(x+2)(x+3)+…… + 1/(x+1998)(x+1999)(写出计算过

网友回答

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)
用裂项相消======以下答案可供参考======
供参考答案1:
=1/x-1/(x+1) +…… + 1/(x+1998)-1/(x+1999)
=1/x-1/(x+1999)
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