Limit of $x_n=0,\!7777...7$ ($n$ is the number of digits $7$) I have a sequence $n$-th member of which equals to $x_n=0,\!777...7$ (where $n$ is a number of digits $7$).
I've successfully proven that this is a Cauchy sequence. That means it converges to a limit. My question is, what is the limit?
I thought that it could be $0,\!78$, but the difference $0,\!78-x_n \ge 0,\!0022$.

Hint: Write $x_n$ as a geometric series (a sum of $7$ times powers of $10$), and use the formula for a geometric series.
