设正整数数列an为一个等比数列,且a2=4,a4=16 求lga(n+1)+lga(n+2)+.+lga(2n)

问题描述:

设正整数数列an为一个等比数列,且a2=4,a4=16 求lga(n+1)+lga(n+2)+.+lga(2n)

显然An=2^n
lga(n+1)+lga(n+2)+.+lga(2n)
=lg(2^(n+1))+...lg(2^(2n))
=(n+1)lg2+...2n*lg2
=lg2*((n+1+2n)*n/2)
=lg2*((3n^2+n)/2)