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數學難題~~求解!!!!!!

Nov 29th 2014, 01:53

1/a+1/b+1/c+1/d+1/e+1/f+1/g+1/h+1/i+1/j=1
首先，a不等於1，因為1/1=1
所以a=2
1/2=3/6
1/b應=2/6，所以b=3
1/a+1/b=5/6=10/12
所以c應=12
1/a+1/b+1/c=11/12=22/24
所以d=24
1/a+1/b+1/c+1/d=23/24=46/48
所以e=48
.
.
.
.
算完後原版應該是這樣:
f=96
g=192
h=384
i=768
j=768
但10個數應該都不相同才對，所以我們要對i動手腳
如果像這樣→原本ix2→1536
所以:
1/a+1/b+1/c+1/d+1/e+1/f+1/g+1/h+1/i
=1/2+1/3+1/12+1/24+1/48+1/96+1/192+1/384+1/1536
=1533/1536
所以1/j+1533/1536應該要=1，故j=1536/3，1/j=3/1536=1/512

綜合一下:
a=2
b=3
c=12
d=24
e=48
f=96
g=192
h=384
i=1536
j=512

參考資料自己

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