Finding $S_{n}$ for this geometric series? Here is what was given to me:
$t_{1}$ = $\frac {1}{256}$
$r$ = $-4$
$n$ = $10$
The formula I used is $S_{n}$ = $\frac {t_{1} (r^{n} - 1)}{r - 1}$
Here's what I did:
$S_{10}$ = $\frac {\frac{1}{256} (-4^{10} - 1)}{-4 - 1}$
$S_{10}$ = $\frac {\frac{1}{256} (-1048576 - 1)}{-5}$
$S_{10}$ = $\frac {\frac{1}{256} (-1048577)}{-5}$
$S_{10}$ = $-\frac{1048577}{256}$ $\div$ $-\frac{5}{1}$
$S_{10}$ = $\frac{209715}{256}$
in the textbook, the answer is a negative. how???
I see what I did wrong. Should I always be using the rule mentioned?

Given:
$t_{1}$ = $\frac {1}{256}$
$r$ = $-4$
$n$ = $10$
$S_{n} = \frac {t_{1} (r^{n} - 1)}{r - 1}$
then $(-4)^{10} = (-1)^{10} \cdot 1048576 = 1048576$ and
\begin{align}
S_{10} &= \frac{1}{256} \, \frac{(-4)^{10} - 1}{-4 -1} \\
&= \frac{1}{256} \, \frac{1048575}{-5} = - \frac{209715}{256}
\end{align}
