- Problem Statement
- Let ##q \geq 2## be an integer. Let ##n = (d_k d_{k-1} \dots d_1 )_(q)## be a q-ary representation of n. Prove that ##nq = (d_k d_{k-1} \dots d_1 0)_(q)##.

- Relevant Equations
- as above for n and nq.

##nq = q(d_1 + d_2 q + d_3 q^2 + \dots + d_k q^{k-1})##

##= d_1 q + d_2 q^2 + d_3 q^3 + \dots + d_k q^k##

##= d_k d_{k-1} \dots d_1 0##

Can someone please explain how to get from line two to line three. This is instructors solution and not sure I understand. Thanks!

##= d_1 q + d_2 q^2 + d_3 q^3 + \dots + d_k q^k##

##= d_k d_{k-1} \dots d_1 0##

Can someone please explain how to get from line two to line three. This is instructors solution and not sure I understand. Thanks!