一道数学题.2004年“我爱数学”少年夏令营的题.1/3+1/5+1/7+1/9+1/11+1/33+1/35+1/45+1/55+1/77

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一道数学题.2004年“我爱数学”少年夏令营的题.1/3+1/5+1/7+1/9+1/11+1/33+1/35+1/45+1/55+1/77
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一道数学题.2004年“我爱数学”少年夏令营的题.1/3+1/5+1/7+1/9+1/11+1/33+1/35+1/45+1/55+1/77
一道数学题.2004年“我爱数学”少年夏令营的题.
1/3+1/5+1/7+1/9+1/11+1/33+1/35+1/45+1/55+1/77

一道数学题.2004年“我爱数学”少年夏令营的题.1/3+1/5+1/7+1/9+1/11+1/33+1/35+1/45+1/55+1/77
1/3+1/5+1/7+1/9+1/11+1/33+1/35+1/45+1/55+1/77
=1/3+1/5+1/7+1/9+1/11+1/(3*11)+1/(5*7)+1/(5*9)+1/(5*11)+1/(7*11)
=1/3+1/5+1/7+1/9+1/11+(8/3-8/11)+(2/5-2/7)+(4/5-4/9)+(6/5-6/11)+(4/7-4/11)
=(1/3+8/3) + (1/5+2/5+4/5+6/5) + (1/7-2/7+4/7) + (1/9-4/9) + (1/11-8/11-6/11-4/11)
=3 + 13/5 + 3/7 - 3/9 - 17/11
=3 + (2+ 3/5) + 3/7 - 1/3 - (1+ 6/11)
=2 + 3/5 + 3/7 + 2/3 + 5/11
=2 + (3*12)/35 + (22+15)/33
=4 + 1/35 + 4/33
=4 + (33+4*35)/(33*35)
=4 + (33+140)/1155
=4 + 173/1155

15147/12705