在等比数列{an}中,若a10a11=4,则数列{㏒1/2底an}的前20项之和

Question

在等比数列{an}中,若a10a11=4,则数列{㏒1/2底an}的前20项之和

Answer 1

log2(an)
sn=log(1/2)(a1)+log(1/2)(a2)+log(1/2)(a3)+.+log(1/2)(a20)
=log(1/2)(a1*a2*a3*.*a20)
=log(1/2)(a10*a11)^10
=log(1/2)(4^10)
=log(1/2)(2^20)
=log(1/2)[(1/2)^(-20)
=-20