数列{xn}满足lgxn+1=1+lgxn,且x,+x2+…x100=100,则lg(x101+x102+…x200为?

问题描述:

数列{xn}满足lgxn+1=1+lgxn,且x,+x2+…x100=100,则lg(x101+x102+…x200为?

lgX(n+1) = 1+lgXn
X(n+1) = 10Xn
所以X101 + X102 +...+ X200 = 10^100*(X1 + X2 +...+ X100) = 10^102
所以lg(X101 + X102 +...+ X200) = 102