Question

已知a/b=c/d=e/f=……=m/n ,且b+d+f+……+n≠0,求证：a+c+e+……+m/b+d+f+……+n

Answer 1

设 a/b=c/d=e/f=……=m/n=k则 a=bk c=dk e=fk.m=nk将上面一串带入,则有 a+c+e+……+m/b+d+f+…+n=bk+dk+fk+.nk/=b+d+f+……+n约分,则 a+c+e+……+m/b+d+f+……+n=k而 k=a/b故 a+c+e+……+m/b+d+f+……+n=a/b...