因?yàn)?a,b,c 成等比數(shù)列,所以 ac=b^2
又因?yàn)閙是a與b的等差中項(xiàng),n是b與c的等差中項(xiàng),所以
m=(a+b)/2,n=(b+c)/2,因此
a/m + c/n
=2a/(a+b) + 2c/(b+c)(通分)
=[2a(b+c)+2c(a+b)]/[(a+b)(b+c)]
=(2ab+2bc+4ac)/(ab+bc+ac+b^2)(由ac=b^2)
=(2ab+2bc+4b^2)/(ab+bc+2b^2)
=2
即 a/m + c/n =2,選B.