证明 等比数列中,m+n=p+q=2k,则aman=apaq=a^2k
问题描述：
证明 等比数列中,m+n=p+q=2k,则aman=apaq=a^2k
答
设公比为t.
aman=[a1t^(m-1)][a1t^(n-1)]
=a1^2t^(m+n-2)
=a1^2t^(2k-2)
=[a1t^(k-1)]^2
=(ak)^2
apaq=[a1t^(p-1)][a1t^(q-1)]
=a1^2t^(p+q-2)
=a1^2t^(2k-2)
=[a1t^(k-1)]^2
=(ak)^2
aman=apaq=(ak)^2