数列﹛an﹜满足a1=3,an=√an-1(n≥2),则log3(a1•a2•···an)=…数列﹛an﹜满足a1=3,an=√an-1(n≥2),则log3(a1•a2•···an)=………?

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/02 18:30:19
数列﹛an﹜满足a1=3,an=√an-1(n≥2),则log3(a1•a2•···an)=…数列﹛an﹜满足a1=3,an=√an-1(n≥2),则log3(a1•a2•···an)=………?
x){6uӎwN{sγ _lۜhhkgcVb=y:өcfN~1P(PM:8}԰v&CMR> Oca/ѐ2M#Qh&Xh HTAPHAHUjX|mS )֩"ӢhhUV "<6P6) FцѼX<;P$n+

数列﹛an﹜满足a1=3,an=√an-1(n≥2),则log3(a1•a2•···an)=…数列﹛an﹜满足a1=3,an=√an-1(n≥2),则log3(a1•a2•···an)=………?
数列﹛an﹜满足a1=3,an=√an-1(n≥2),则log3(a1•a2•···an)=…
数列﹛an﹜满足a1=3,an=√an-1(n≥2),则log3(a1•a2•···an)=………?

数列﹛an﹜满足a1=3,an=√an-1(n≥2),则log3(a1•a2•···an)=…数列﹛an﹜满足a1=3,an=√an-1(n≥2),则log3(a1•a2•···an)=………?
an =√(a(n-1)
logan = (1/2)loga(n-1)
{logan} 是等比数列,q=1/2
logan = (1/2)^(n-1) .(loga1)
= (1/2)^(n-1)
log(a1.a2.an)
=loga1+loga2+...+logan
=1+1/2+.+(1/2)^(n-1)
= 2[1-(1/2)^n]