等比数列中,若a1=1000,a3=10,bn=1/n(lga2+lga4+……+lga2n),则数列{bn}的前n项和的最大值________
问题描述:
等比数列中,若a1=1000,a3=10,bn=1/n(lga2+lga4+……+lga2n),则数列{bn}的前n项和的最大值________
答
a1=1000
a3=10
q=1/10
bn=1/n(lga2+lga4+……+lga2n)
=1/n(lg(a2*a4*a6…………a2n)
=1/n(lg(a1^n*q^n^2)
=1/n(lg10^(3n-n^2))
=1/n(3n-n^2)
=3-n
所以最大值为3