已知等比数列{an}的各项都是正数,证明数列{lgan}为等比数列,若a1×a10= ：根号10,求lga1+lga2+...lg_数学解答

已知等比数列{an}的各项都是正数,证明数列{lgan}为等比数列,若a1×a10= ：根号10,求lga1+lga2+...lga10

人气：165 ℃　时间：2020-08-30 06:27:47

解答

为等差吧 {an}是等比数列所以an^2=an+1×an-1lgan^2=lg(an+1×an-1)2 lgan= lgan+1+ lgan-1{ lgan }是等差数列Lga1+… lga10= lg(a1×.a10)a1×a10=根号10a1×.a10=10^2.5所以Lga1+… lga10= lg(a1×.a10)=2.5...