1/2*4+1/4*6+1/6*8+1/8*10+1/10*12+1/12*14+1/14*16

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1/2*4+1/4*6+1/6*8+1/8*10+1/10*12+1/12*14+1/14*16
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1/2*4+1/4*6+1/6*8+1/8*10+1/10*12+1/12*14+1/14*16
1/2*4+1/4*6+1/6*8+1/8*10+1/10*12+1/12*14+1/14*16

1/2*4+1/4*6+1/6*8+1/8*10+1/10*12+1/12*14+1/14*16
1/2*4+1/4*6+1/6*8+1/8*10+1/10*12+1/12*14+1/14*16
=(1/2)*(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12+1/12-1/14+1/14-1/16)
=(1/2)*(1/2-1/16)
=7/32

1/n(n+2)=(1/n-1/(n+2))/2
所以:1/2*4+1/4*6+1/6*8+1/8*10+1/10*12+1/12*14+1/14*16
=(1/2-1/16)/2=7/32