若a1/b1=a2/b2=a3/b3=.=an/bn   则a1/b1=a2/b2=...=(a1+a2+a3+...+an)/(b1+b2+b3+...+bn)怎么证?

问题描述:

若a1/b1=a2/b2=a3/b3=.=an/bn   则a1/b1=a2/b2=...=(a1+a2+a3+...+an)/(b1+b2+b3+...+bn)怎么证?

令a1/b1=a2/b2=a3/b3=.=an/bn=n/m,n,m互质.则有a1=t1*n,a2=t2*n,.,an=tn*n.b1=t1*m,b2=t2*m,...,bn=tn*m(a1+a2+a3+...+an)/(b1+b2+b3+...+bn)=(t1+t2+...+tn)n/(t1+t2+...+tn)m=n/m