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?
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. I feel like an epsilon argument might work here? But how will the number of terms help me?