1/1x4 +1/4x7+1/7x10+......+1/100x103 急用啊
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1/(1×4)+1/(4×7)+1/(7×10)+……+1/(100×103)
=(1/3)×3/(1×4)+(1/3)×3/(4×7)+(1/3)×3/(7×10)+……+(1/3)×3/(100×103)
=(1/3)×[3/(1×4)+3/(4×7)+3/(7×10)+……+3/(100×103)]
=(1/3)×[(1-1/4)+(1/4-1/7)+(1/7-1/10)+……+(1/100-1/103)]
=(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
=(1/3)×3/(1×4)+(1/3)×3/(4×7)+(1/3)×3/(7×10)+……+(1/3)×3/(100×103)
=(1/3)×[3/(1×4)+3/(4×7)+3/(7×10)+……+3/(100×103)]
=(1/3)×[(1-1/4)+(1/4-1/7)+(1/7-1/10)+……+(1/100-1/103)]
=(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
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