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计算1/1+2+1/1+2+3+...+1/1+2+3+...+100请给予准确答案,

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1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+······+1/(1+2+3······+100)=1/(3×2/2)+1/(4×3/2)+1/(5×4/2)+······+1/(101×100/2)=2×[1/(2×3)+1/(3×4)+1/(4...