若数列{xn}满足lgxn+1=1+lgxn(n∈N*),且x1+x2+…+x100=100,则lg(x101+x102+…+x200)的值为_.

问题描述:

若数列{xn}满足lgxn+1=1+lgxn(n∈N*),且x1+x2+…+x100=100,则lg(x101+x102+…+x200)的值为______.

∵lgxn+1-lgxn=1,∴lg

xn+1
xn
=1,
∴lg(x101+x102+…+x200
=lg[(x1+x2+…+x100)×10100]
=lg(100×10100
=lg10102
=102
答案:102.