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设正项等比数列{an}的前n项积为tn,若t9=1则a4×a6
人气:417 ℃ 时间:2020-07-24 09:50:34
解答
a(n) = aq^(n-1),a>0,q>0.
t(n) = a(1)a(2)...a(n-1)a(n) = a*aq*...*aq^(n-2)*aq^(n-1) = a^nq^[1+2+...+(n-1)]
= a^nq^[n(n-1)/2].
1 = t(9) = a^9q^[36] = [aq^4]^9,aq^4 = 1.
a(4)a(6) = aq^3*aq^5 = a^2q^8 = [aq^4]^2 = 1^2 = 1.
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