4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255
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4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255
4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255
4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255
参考一下.
4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255=(2×2)/(1×3)+(4×4)/(3×5)+...(14×14)/(13×15)+(16×16)/(15×17)=(2-2/3)+(8/3-8/5)+...+(98/13-98/15)+(128/15-128/17)=8×2-128/17=144/17
4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255
=1+1/3+1+1/15++1+1/35+1+1/63+1+1/99+1+1/143+1+1/195+1+1/255
=8+1/3+(1/3-1/5)×1/2+(1/5-1/7)1/2+(1/7-1/9)×1/2+(1/9-1/11)×1/2+(1/11-1/13)×1/2+...
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4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255
=1+1/3+1+1/15++1+1/35+1+1/63+1+1/99+1+1/143+1+1/195+1+1/255
=8+1/3+(1/3-1/5)×1/2+(1/5-1/7)1/2+(1/7-1/9)×1/2+(1/9-1/11)×1/2+(1/11-1/13)×1/2+(1/13-1/15)×1/2+(1/15-1/17)×1/2
=8+1/3+(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15+1/15-1/17)×1/2
=8+1/3+(1/3-1/17)×1/2
=8+1/3+1/6-1/34
=8+34/102+17/102-3/102
=8+8/17
=8又8/17
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