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问题: 数学问题

1-1/2=1/2=1/1*2
1/2-1/3=1/6=1/2*3
1/3-1/4=1/12=1/3*4
..............
8/1*5+8/5*9+8/9*13+8/13*17=?????

解答:

1/1-1/2 = 1/2 = 1/1•2
1/2-1/3 = 1/6 = 1/2•3
1/3-1/4 = 1/12 =1/3•4
...

 8/1•5 + 8/5•9 + 8/9•13 + 8/13•17
= 2(5-1)/1•5 + 2(9-5)/5•9 + 2(13-9)/9•13 + 2(17-13)/13•17
= 2(1-1/5) + 2(1/5-1/9) + 2(1/9-1/13) + 2(1/13-1/17)
= 2(1-1/17)
= 32/17