MathDB

Set

T=\{0,1,2,3,4,5,6\},M=\left\{\frac{a_1}{7}+\frac{a_2}{7^2}+\frac{a_3}{7^3}+\frac{a_4}{7^4}|a_i\in T,i=1,2,3,4\right\}

. Put all elements in

M

in order: from small to large, then the 2005th number is

\text{(A)}\frac{5}{7}+\frac{5}{7^2}+\frac{6}{7^3}+\frac{3}{7^4}

\text{(B)}\frac{5}{7}+\frac{5}{7^2}+\frac{6}{7^3}+\frac{2}{7^4}

\text{(C)}\frac{1}{7}+\frac{1}{7^2}+\frac{0}{7^3}+\frac{4}{7^4}

\text{(D)}\frac{1}{7}+\frac{1}{7^2}+\frac{0}{7^3}+\frac{3}{7^4}

Problem Statement