1/1X2+1/2X3+1/3X4...+1/100X101+101X102怎么算

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1/1X2+1/2X3+1/3X4...+1/100X101+101X102怎么算1/1X2+1/2X3+1/3X4...+1/100X101+101X102怎么算1/1X2+1/2X3+1/3X4.

1/1X2+1/2X3+1/3X4...+1/100X101+101X102怎么算
1/1X2+1/2X3+1/3X4...+1/100X101+101X102怎么算

1/1X2+1/2X3+1/3X4...+1/100X101+101X102怎么算
1/1*2+1/2*3+...+1/(n*(n+1))
1/(n*(n+1)=1/n-1/(n+1)
所以原式=1-1/2+1/2-1/3+...-1/101+1/101-1/102
=1-1/102=101/102

1-1/2+1/2-1/3+1/3-1/4+.....+1/100-1/101+1/101-1/102
=1-1/102
=101/102