# Pointwise convergence of the series $f_n(x)=x^n$

I know that the sequence $$f_n(x) = x^n$$ Converges pointwise to $$f(x) = \begin{cases} 0 & 0\leq x < 1 \\ 1 & x=1\end{cases}$$ in $[0,1]$.

My question is - is it right to say that the sequence converges to the line $x = 1$ for $x\in(1,\infty)$?

Edit: Confused with sequence not series

• Yes I mixed another exercise I had, sorry. – JonTrav Jun 13 '15 at 7:11

If $x>1$, the sequence $x^n$ diverges.
The line $x=1$ is always going to be distance 1 away from the point $(2,2^n)$. So there's no uniformity.
• I know that, but when graphing $x^n$ for $x>1$ as $n$ gets larger the graph gets more and more perpendicular to the $x$-axis. I know that it does not converge to any function, I asked about a curve – JonTrav Jun 13 '15 at 7:13