Question

高二数学，关于等比数列

已知数列{an} 是一个以q（q>0)为公比、以a1(a1>0)为首项的等比数列，求lga1+lga2+……+lgan

Answer 1

lga1+lga2+……+lgan
=lga1+lgqa1+lgq^2a1……+lgq^(n-1)a1
=nlga1+lgq+lgq^2+.....+lgq^(n-1)
=nlga1+lgq+2lgq+3lgq+.....+(n-1)lgq
=nlga1+(1/2)lgq*n(n-1)

Answer 2

=lg(a1a2……an)
=lg[(a1)^n]*[q^(1+2+3+……+n-1)]
=nlga1+[n(n-1)/2]*lgq