1/1x4十1/4x7+1/7x10+……1/100X103这题怎么做

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1/1x4十1/4x7+1/7x10+……1/100X103这题怎么做
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1/1x4十1/4x7+1/7x10+……1/100X103这题怎么做
1/1x4十1/4x7+1/7x10+……1/100X103这题怎么做
 

1/1x4十1/4x7+1/7x10+……1/100X103这题怎么做
裂项法:
1/1x4十1/4x7+1/7x10+……1/100X103
=1/3×(1-1/4+1/4-1/7+1/7-1/10+……+1/100-1/103)
=1/3×(1-1/103)
=1/3×102/103
=34/103