1/1x4+1/4x7+……+1/91x94=?

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1/1x4+1/4x7+……+1/91x94=?
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1/1x4+1/4x7+……+1/91x94=?
1/1x4+1/4x7+……+1/91x94=?

1/1x4+1/4x7+……+1/91x94=?
1/1x4=(1/3)*(1/1-1/4)
1/4*7=(1/3)(1/4-1/7)
..
1/91*94=(1/3)(1/91-1/94)
所以:
1/1x4+1/4x7+……+1/91x94
=(1/3)*(1/1-1/4+1/4-1/7+..+1/91-1/94)
=(1/3)(1-1/94)
=31/94

采用裂项法
原式=1/3(1/1-1/4+1/4-1/7++1/91-1/94)=31/94