已知等比数列{an}的各项均为正数
已知等比数列{an}的各项均为正数,且a5a6=9,求log3a1 + log3a2+ ……+ lo已知等比数列{an}的各项均为正数,且a5a6=9,求log3a1 + log3a2+ ……+ log3a10的值。 下标不能显示,请看附件。 谢谢.
因为a5a6=9--->a1^2q^9=9 又a1a10=a1*a1q^9=9,a2a9=a1q*a1q^8=a1^2*q^9=9,a3a8=a1^2*q^9=9, a4a7=a1^2*q^9=9 所以a1a2a2……a9=(a5a6)^5=9^5=3^10 log(3)a1+log(3)a2+……+log(3)a9 =log(3)(a1a2……a9) =log(3)3^10 =10.
log3a1+log3a2+……+log3a10 =log3(a1a2……a10) =log3(a1a10a2a9……a5a6) =log3(a5a6^5) =5log3(a5a6) =5log3(9) =5*2 =10
答:4/3 a/q2+a/q+a+aq+aq2=211/27 q2/a+q/a+1/a+1/aq+1/aq2=211/48 aq2+aq+a+a/q+a/q2=21...详情>>
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