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

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