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

来源：学生作业帮助网编辑：作业帮时间：2024/05/03 09:51:00

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

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

=1/x-1/(x+1) +…… + 1/(x+1998)-1/(x+1999)
=1/x-1/(x+1999)

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