问题: 请巧算
请写出计算步骤，谢谢。
1/（2×7）+1/（7×12）+1/（12×17）+1/（17×22）+1/（22×27）=
128×（1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288）=
1+（6×3+1）/6+（12×5+1）/12+（20×7+1）/20+（30×9+1）/30+（42×11+1）/42+（56×13+1）/56+（72×15+1）/72+（90×17+1）/90=
解答:
1/（2×7）+1/（7×12）+1/（12×17）+1/（17×22）+1/（22×27）
= 5[(1/2-1/7+1/7-1/12+1/12-1/17+1/17-1/22+1/22-1/27)]
=5(1/2-1/27)=125/54
128×（1/8+1/24+1/48+1/80+1/120+1/168+1/224+1/288）
=128*(1/8)[1+1/3+1/6+1/10+1/15+1/21+1/28+1/36]
=128*(1/8)[1+2(1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9))]
=128*(1/8)[1+2(1/2-1/3+1/3-1/4+...+1/8-1/9]
=128*(1/8)[1+2(1/2-1/9)]
=128*(1/8)[1+1-2/9]
=128*(1/8)(16/9)
=256/9
1+（6×3+1）/6+（12×5+1）/12+（20×7+1）/20+（30×9+1）/30+（42×11+1）/42+（56×13+1）/56+（72×15+1）/72+（90×17+1）/90
= 1+3+1/6++5+1/12+7+1/20+9+1/30+11+1/42+13+1/56+15+1/72+17+1/90
=(1+3+5+...+17)+1/(2*3)+1/(3*4)+...1/(9*10)
=(1+3+5+...+17)+1/2-1/3+1/3-1/4+...+1/9-1/10)
=(1+17)9/2+1/2-1/10
=81+2/5
=407/5
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