数列求证题设等差数列{An}的公差为d,d>0,数列{B}是公比为q等比数列,且B1=A1>0.若A2=B2,求证：当n>2时,An

Question

数列求证题
设等差数列{An}的公差为d,d>0,数列{B}是公比为q等比数列,且B1=A1>0.
若A2=B2,求证：当n>2时,An

Answer 1

数学归纳法
n=3
b3-a3
=b2^2/b1-(2a2-a1)
=a2^2/a1-(2a2-a1) (通分,化简)
=(a1-a2)^2/a1>0
假设n=k-1是成立,即b(k-1)>a(k-1)
bk-ak
=b(k-1)b2/b1-a(k-1)-(a2-a1)
>a(k-1)a2/a1-a(k-1)-(a2-a1)
=[a(k-1)/a1 - 1](a2-a1))>0
bk > ak
证毕