1/（1x3）+1/（2x4）+1/（3x5）+1/(4x6)+1/(5x7)+1/(6x8)的答案
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1/(1x3)+1/(2x4)+1/(3x5)+1/(4x6)+1/(5x7)+1/(6x8)
=[1/(1*3)+1/(2*4)+1/(3*5)+1/(4*6)+1/(5*7)+1/(6*8)]*[2*(1/2)]
=[2/(1*3)+2/(2*4)+2/(3*5)+2/(4*6)+2/(5*7)+2/(6*8)]*(1/2)
=[(1-1/3)+(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+(1/5-1/7)+(1/6-1/8)]*(1/2)
=1+1/2-1/7-1/8
=153/56
=[1/(1*3)+1/(2*4)+1/(3*5)+1/(4*6)+1/(5*7)+1/(6*8)]*[2*(1/2)]
=[2/(1*3)+2/(2*4)+2/(3*5)+2/(4*6)+2/(5*7)+2/(6*8)]*(1/2)
=[(1-1/3)+(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+(1/5-1/7)+(1/6-1/8)]*(1/2)
=1+1/2-1/7-1/8
=153/56
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