计算1/X(X+1)+1/(X+1)(X+2)+.+1/(X+99)(X+100) 其中x=100 速度求答案,求过程
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计算1/X(X+1)+1/(X+1)(X+2)+.+1/(X+99)(X+100) 其中x=100 速度求答案,求过程
![计算1/X(X+1)+1/(X+1)(X+2)+.+1/(X+99)(X+100) 其中x=100 速度求答案,求过程](/uploads/image/z/11111468-68-8.jpg?t=%E8%AE%A1%E7%AE%971%2FX%28X%2B1%29%2B1%2F%28X%2B1%29%28X%2B2%29%2B.%2B1%2F%28X%2B99%29%28X%2B100%29+%E5%85%B6%E4%B8%ADx%3D100+%E9%80%9F%E5%BA%A6%E6%B1%82%E7%AD%94%E6%A1%88%2C%E6%B1%82%E8%BF%87%E7%A8%8B)
1/X(X+1)+1/(X+1)(X+2)+.+1/(X+99)(X+100)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+99)-1/(x+100)
=1/x-1/(x+100)
=1/100-1/(100+100)
=1/100-1/200
=1/200
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+99)-1/(x+100)
=1/x-1/(x+100)
=1/100-1/(100+100)
=1/100-1/200
=1/200
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