Possible Duplicate:
Value of $\sum\limits_n x^n$
In my lecture notes:
$a_n = \frac{1}{2^n}, \qquad \sum_{n-1}^{\infty} a_n = \lim_{n\to\infty} (1-\frac{1}{2^n}) = 1$
How do I get $(1-\frac{1}{2^n})$?
A similar example given is
$a_n = 2^{n-1}, \qquad \sum_{n-1}^{\infty} a_n = \lim_{n\to\infty} (2^n - 1)$
How do I get these?