Question

如果a/b=c/d=…=m/n,为什么(b+d+…+n不=0),为什么(a+c+…+m)/(b+d+…+n)=a/b

Answer 1

由题,设a/b=c/d=…=m/n=k

则,a=bk,c=dk,……,m=nk

又,b+d+…+n≠0

所以,

(a+c+…+m)/(b+d+…+n)

=(bk+dk+…+nk)/(b+d+……+n)

=k

=a/b

所以,(a+c+…+m)/(b+d+…+n)=a/