2/3+2/15+2/35+2/63+2/99+2/132

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2/3+2/15+2/35+2/63+2/99+2/132
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2/3+2/15+2/35+2/63+2/99+2/132
2/3+2/15+2/35+2/63+2/99+2/132

2/3+2/15+2/35+2/63+2/99+2/132
原式=2/(1x3)+2/(3x5)+2/(5x7)+2/(7x9)+2/(9x11)+2/(11x12)
=(3-1)/(1x3)+(5-3)/(3x5)+(7-5)/(5x7)+(9-7)/(7x9)+(11-9)/(9x11)+2/(11x12)
=(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+2/(11x12)
=1+(1/3-1/3)+(1/5-1/5)+(1/7-1/7)+(1/9-1/9)-1/11+2/(11x12)
=10/11+2/(11x12)
=(120+2)/(11x12)
=61/66.

13分之12

2/3+2/15+2/35+2/63+2/99+2/132
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13
=1-1/13
=12/13