计算题:1/3+1/15+1/35+1/63+1/99+1/143
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计算题:1/3+1/15+1/35+1/63+1/99+1/143
![计算题:1/3+1/15+1/35+1/63+1/99+1/143](/uploads/image/z/7566508-28-8.jpg?t=%E8%AE%A1%E7%AE%97%E9%A2%98%EF%BC%9A1%2F3%2B1%2F15%2B1%2F35%2B1%2F63%2B1%2F99%2B1%2F143)
1/3+1/15+1/35+1/63+1/99+1/143
=1/2*[2*(1/3+1/15+1/35+1/63+1/99+1/143)]
=1/2*[2/3+2/15+2/35+2/63+2/99+2/143]
=1/2*[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)]
=1/2*(1-1/13)
=6/13
=1/2*[2*(1/3+1/15+1/35+1/63+1/99+1/143)]
=1/2*[2/3+2/15+2/35+2/63+2/99+2/143]
=1/2*[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)]
=1/2*(1-1/13)
=6/13