1/2,1/4,1/12,1/20,······前30个数的和是( ).
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1/2,1/4,1/12,1/20,······前30个数的和是( ).
1/2+1/6+1/12+1/20+...
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/30-1/31)
=1-1/2+1/2-1/3+1/3-1/4+...+1/30-1/31
=1-1/31
=30/31
1/2,1/4,1/12,1/20,······前30个数的和是( ).
1/2+1/6+1/12+1/20+...
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/30-1/31)
=1-1/2+1/2-1/3+1/3-1/4+...+1/30-1/31
=1-1/31
=30/31