计算1/x(x+1)+1/(x+1)(x+2)+...+1/(x+1998)(x+1999)当x=1时,该代数式的值

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计算1/x(x+1)+1/(x+1)(x+2)+...+1/(x+1998)(x+1999)当x=1时,该代数式的值
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计算1/x(x+1)+1/(x+1)(x+2)+...+1/(x+1998)(x+1999)当x=1时,该代数式的值
计算1/x(x+1)+1/(x+1)(x+2)+...+1/(x+1998)(x+1999)当x=1时,该代数式的值

计算1/x(x+1)+1/(x+1)(x+2)+...+1/(x+1998)(x+1999)当x=1时,该代数式的值
1/x(x+1)+1/(x+1)(x+2)+...+1/(x+1998)(x+1999)
=1/1×2+1/2×3+1/3×4+……+1/1999×2000
=1-1/2+1/2-1/3+1/3-1/4+……+1/1999-1/2000
=1-1/2000
=1999/2000

1/x(x+1)+1/(x+1)(x+2)+...+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)
当x=1时
原式=1-1/2000=1999/2000

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