Consider the sum

where we sum over all

where

doesn't have the digit 9 in its decimal expansion. Show that the series converges. Hint: How many terms are there in the sum where

has exactly

digits?

My Work:

I see that the hint is 9^k-1 since every digit can be anything from 0-8 but not all digits can be 0. The question seems a little confusing since it talks about the sum and then asks if the series converges.. I feel like an epsilon argument might work here? But how will the number of terms help me?