已知1/a.1/b.1/c成等差数列.求证.(b+c)/a.(c+a)/b.(a+b)/c也成等差数列
1/a+d=1/b=1/c-d
1/a=1/b-d
1/c=1/b+d
a=b/(1-bd)
c=b/(1+bd)
(b+c)/a+(a+b)/c-2(c+a)/b=[b+b/(1+bd)][(1-bd)/b]+[b/(1-bd)+b][(1+bd)/b]-2[b/(1+bd)+b/(1-bd)]/b
=[1+1/(1+bd)](1-bd)+[1/(1-bd)+1](1+bd)-2[1/(1+bd)+1/(1-bd)]
=(1-bd)+(1-bd)/(1+bd)+(1+bd)/(1-bd)+(1+bd)-2/(1+bd)-2/(1-bd)
=2+(1-bd-2)/(1+bd)+(1+bd-2)/(1-bd)
=2-1-1
=0