数列an满足a1=8,an=根号an-1,则log(a1a2.an)底数是2

Question

数列an满足a1=8,an=根号an-1,则log(a1a2.an)
底数是2

Answer 1

log(a1a2.an)
=loga1+loga2+loga3+……+logan
=loga1+log√a1+log√a2+……+log√an-1
=loga1+½loga1+½loga2+……+½logan-1
=loga1+½loga1+(½)²loga1+……+(½)^(n-1)loga1
=[1+1/2+(½)²+……+(½)^(n-1)]loga1
=[(1-½ⁿ)/(1-½)]log8
=2(1-½ⁿ)*log8

由于你这没写对数的底数是什么,所以我没法算log8了,但到这你应该会算下面的了,不明白再追问哈!