1/1×5+1/5×9+1/9×13+1/13×17+1/17×211/1*5+1/5*9+1/9*13+1/13*17+1/17*21=1/4*(1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21)=1/4*(1-1/21)=1/4*20/21=5/21为什么
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1/1×5+1/5×9+1/9×13+1/13×17+1/17×211/1*5+1/5*9+1/9*13+1/13*17+1/17*21=1/4*(1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21)=1/4*(1-1/21)=1/4*20/21=5/21为什么
1/1×5+1/5×9+1/9×13+1/13×17+1/17×21
1/1*5+1/5*9+1/9*13+1/13*17+1/17*21
=1/4*(1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21)
=1/4*(1-1/21)
=1/4*20/21
=5/21为什么
1/1×5+1/5×9+1/9×13+1/13×17+1/17×211/1*5+1/5*9+1/9*13+1/13*17+1/17*21=1/4*(1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21)=1/4*(1-1/21)=1/4*20/21=5/21为什么
因为:
1/1×5可写为1/4*(1-1/5)
1/5×9可写为1/4*(1/5-1/9)
1/9×13可写为1/4*(1/9-1/13)
1/13×17可写为1/4*(1/13-1/17)
1/17×21可写为1/4*(1/17-1/21)
所以提出一个1/4即成为上面的形式
设甲乙两地相距x千米,则可列方程为_________________
1/n(n+4)=(1/n-1/n+4)/4.
1/5*1/9+1/9*1/13+1/13*1/17+.1/101*1/105
1*5/1+5*9/1+9*13/1+13*17/1+17*21/1
1/1*5+1/5*9+1/9*13+1/13*17+1/17*21
1*5/1+5*9/1+9*13/1+13*17/1+.45*49/1
1/1×5+1/5×9+1/9×13+1/13×17+...+1/25×29=
1/5*9+1/9*13+.+1/101*105
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计算:1/3*5+1/5*7+1/7*9+1/9*11+1/11*13
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1/1*5+1/5*9+1/9*13+.+1/101*105
1/1×5+1/5×9+1/9×13+...+1/2009×2013
1×5/1+5×9/1+9×13/1+…+2009×2013/1
1/1*5+1/5*9+1/9*13+.+1/55*59
1/1*5+1/5*9+1/9*13+.+1/55*59
1/1*5+1/5*9+1/9*13+.+1/33*37
1/1×5+1/5×9+1/9×13……+1/33×37 简便计算