设正整数列｛an｝为一个等比数列且a2=4,a4=16求lgan+1 +lgan+2 +...+lg2n
问题描述：
设正整数列｛an｝为一个等比数列且a2=4,a4=16求lgan+1 +lgan+2 +...+lg2n
答
正整数列｛an｝为一个等比数列且a2=4,a4=16
a2=a1*q=4
a4=a1*q^3=16q=2
an=2^n
lgan+1 +lgan+2 +...+lg2n
=lg(2^(n+1)*2^(n+2)*……*2^(2n))
=lg(2^(n+1+n+2+……+2n))
=lg2^((3n+1)*n)/2