3分之一加15分之一加35分之一加63分之一加99分之一加143分之一加195分之一加255分之一等于多少呀

17分之8

1/3+1/15+1/35+1/63+1/99+1/143+1/195+1/255
=1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1(9×11)+1/(11×13)
+1/(13×15)+1/(15×17)
=(1/1-1/3)×1/2+(1/3-1/5)×1/2+(1/5-1/7)×1/2+……+(1/15-1/17)×1/2
=(1-1/3+1/3-1/5+1/5-1/7+……+1/15-1/17)×1/2
=(1-1/17)×1/2
=16/17×1/2
=8/17
公式：
1/3+1/15+1/35+1/63+……+1/n(n+2) （n>1，n是奇数）
=1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+……+1/n(n+2)
=(1/1-1/3)×1/2+(1/3-1/5)×1/2+(1/5-1/7)×1/2+……+[1/n-1/(n+2)]×1/2
=[1-1/3+1/3-1/5+1/5-1/7+……+1/n-1/(n+2)]×1/2
=[1-1/(n+2)]×1/2
=(n+1)/2(n+2)
这里：n=15
和=(15+1)/(2×17)=8/17

原式＝1/（1x3）+1/（3x5）+1/（5x7）+1/（7x9）+1/（9x11）+1/（11x13）+1/（13x15）+1/（15x17）=(1-2/3)+(2/3-3/5)+(3/5-4/7)+(4/7-5/9)+(5/9-6/11)+(6/11-7/13)+(7/13-8/15)+ (8/15-9/17)＝1-9/17＝8/17...

1/3+1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)+1/(13*15)+1/(15*17)
=(1/2)*[(1-1/3)+(1/3-1/5)]+.....+(1/13-1/15)+(1/15-1/17)
=(1/2)*(1-1/3+1/3-1/5+1/5-1/7+...+1/13-1/15+1/15-1/17)
=(1/2)*(1-1/17)=8/17