1/3+1/8+1/15+1/24+.1/9800

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1/3+1/8+1/15+1/24+.1/9800
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1/3+1/8+1/15+1/24+.1/9800
1/3+1/8+1/15+1/24+.1/9800

1/3+1/8+1/15+1/24+.1/9800
原式=[1/(1×3)+1/(3×5)+.+1/(97×99)]+[1/(2×4)+1/(4×6)+.+1/(98×100)]
=(1-1/3+1/3-1/5+1/5-1/7+.+1/97-1/99)+(1/2-1/4+1/4-1/6+.+1/98-1/100)
=1-1/99+1/2-1/100
=14651/9900