1/x(x+1+1/(x+1)(x+2)+···1/(x+99)(x+100)计算

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1/x(x+1+1/(x+1)(x+2)+···1/(x+99)(x+100)计算1/x(x+1+1/(x+1)(x+2)+···1/(x+99)(x+100)计算1/x(x+1+1/(x+1)(x+

1/x(x+1+1/(x+1)(x+2)+···1/(x+99)(x+100)计算
1/x(x+1+1/(x+1)(x+2)+···1/(x+99)(x+100)计算

1/x(x+1+1/(x+1)(x+2)+···1/(x+99)(x+100)计算
原式通分
1/x(x+1)=1/x-1/(x+1)
1/(x+1)(x+2)=1/(x+1)-1/(x+2)
以此类推
原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)+……+1/(x+99)-1/(x+100)
=1/x-1/(x+100)




如图

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