奧數～ 20分

1.333333xA=2AAAAA7
可看尾數:3xA=7
所以A=9
2.2/3+2/15+2/35+2/63+2/99+2/11
=2/(1x3)+2/(3x5)+2/(5x7)+2/(7x9)+2/(9x11)+2/11
=2/1-2/3+2/3-2/5+2/5-2/7+2/7-2/9+2/9-2/11+2/11
=2/1
=2
***d/n(n+d)=1/n-1/n+d***
3.(1,1/2007x3.6+3,3/5x8,2006/2007)/(9,2/5)/(3,4/4)
=(1,1/2007x3.6+3.6x8,2006/2007)/(9,2/5)/(3,4/4)
=3.6x(1,1/2007+8,2006/2007)/(9,2/5)/(3,4/4)
=3.6x10/(9,2/5)/(3,4/4)
=36/(9,2/5)/(3,4/4)
=36/(9,2/5)/4
=36/4/(9,2/5)
=9/(9,2/5)
=9/(47/5)
=9x(5/47)
=45/47
***分數和帶分數我用括號括下，以免混淆。***

1) A = 9, 因為看個位的3, 只有乘9, 才會出7字的個位
2)
2/3 ( 1 + 1/5) + 2/7 ( 1/5 + 1/9 ) + 2/11 ( 1/9 + 1)
2/3 ( 6/5 ) + 2/7 ( 14 /45 ) + 2/11 ( 10 /9 )
4/5 + 4/45 + 20/99
40/45 + 20/99
20/9 ( 2/5 + 1/11)
20/9 ( 27 /55)
ans : 60/55