有n个正分数.a1/b1〈a2/b2〈a3/b3〈...〈an/bn.证明a1/b2〈(a1+a2+.+an)/(b1+b2+.bn)〈an/bn

问题描述:

有n个正分数.a1/b1〈a2/b2〈a3/b3〈...〈an/bn.证明a1/b2〈(a1+a2+.+an)/(b1+b2+.bn)〈an/bn
bi>0

证明:由已知,
a(i),b(i)>0,i=1,2,...,n.
令 x(i) =a(i)/b(i),i=1,2,...,n,
则 a(i) =b(i) *x(i),i=1,2,...,n.
且 x(1)