怎么计算,(1-1/2)+(1/2-1/3)+(1/3-1/4)+.(1/1999-1/2000)怎么计算啊,

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怎么计算,(1-1/2)+(1/2-1/3)+(1/3-1/4)+.(1/1999-1/2000)怎么计算啊,怎么计算,(1-1/2)+(1/2-1/3)+(1/3-1/4)+.(1/1999-1/2

怎么计算,(1-1/2)+(1/2-1/3)+(1/3-1/4)+.(1/1999-1/2000)怎么计算啊,
怎么计算,(1-1/2)+(1/2-1/3)+(1/3-1/4)+.(1/1999-1/2000)
怎么计算啊,

怎么计算,(1-1/2)+(1/2-1/3)+(1/3-1/4)+.(1/1999-1/2000)怎么计算啊,
(1-1/2)+(1/2-1/3)+(1/3-1/4).+(1/1999-1/2000)
=1-1/2+1/2-1/3+1/3-1/4+……+1/1998-1/1999+1/1999-1/2000
=1-(1/2-1/2)-(1/3-1/3)-.(1/1999-1/1999)-1/2000
=1-1/2000
=1999/2000

(1-1/2)+(1/2-1/3)+(1/3-1/4)+。。。。。(1/1999-1/2000)
=1+[-1/2+1/2]+[-1/3+1/3]+[-1/4+1/4]+...。。。。。[-1/1999+1/1999]-1/2000)
=1 - 1/2000
=1999/2000

把括号展开:1-1/2+1/2-1/3+1/3-1/4+。。。。。+1/1999-1/2000
=1-1/2000
=1999/2000