1/15+1/35+1/63+1/99+1/143+1/195的简便算法
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![1/15+1/35+1/63+1/99+1/143+1/195的简便算法](/uploads/image/z/43459-43-9.jpg?t=1%2F15%2B1%2F35%2B1%2F63%2B1%2F99%2B1%2F143%2B1%2F195%E7%9A%84%E7%AE%80%E4%BE%BF%E7%AE%97%E6%B3%95)
1/15+1/35+1/63+1/99+1/143+1/195的简便算法
1/15+1/35+1/63+1/99+1/143+1/195的简便算法
1/15+1/35+1/63+1/99+1/143+1/195的简便算法
原式=1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)+1/(13*15)
=1/2*(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)
=1/2*(1/3-1/15)
=1/2*4/15=2/15
解:原式=1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)+1/(13*15)
=1/2*(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)
=1/2*(1/3-1/15)
=1/2*4/15=2/15