1/2x4十1/4x6十…十1/100X102

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1/2x4十1/4x6十…十1/100X102
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1/2x4十1/4x6十…十1/100X102
1/2x4十1/4x6十…十1/100X102

1/2x4十1/4x6十…十1/100X102
1/2x4=1/2(1/2-1/4)
1/4x6=1/2(1/4-1/6)
以此类推
1/100X102=1/2(1/100-1/102)
所以
1/2x4十1/4x6十…十1/100X102
=1/2(1/2-1/4)+1/2(1/4-1/6)十…十1/2(1/100-1/102)
=1/2(1/2-1/102)
=25/102