How do I solve this geometric series I have this geometric series $2+1+ \frac{1}{2}+ \frac{1}{4}+...+ \frac{1}{128}$to solve. So I extract the number two and get $2(\frac{1}{2}^0+ \frac{1}{2}^1+...+ \frac{1}{2}^7)$
I use the following formula $S_n= \frac{x^{n+1}-1}{x-1}$ so I plug in the values in this formula and get $S_n= 2\frac{\frac{1}{2}^{7+1}-1}{\frac{1}{2}-1}$ but the result is not correct.
What did I do wrong?
Thanks!!

$$S=2+1+ \frac{1}{2}+ \frac{1}{4}+...+ \frac{1}{128}$$
Now if we subtract $2$ from both sides of the equation we get
$$S-2=1+ \frac{1}{2}+ \frac{1}{4}+...+ \frac{1}{128}$$
$$S-2=\frac{1}{2}\cdot \left(2+1+ \frac{1}{2}+ \frac{1}{4}+...+ \frac{1}{64}\right)$$
Now notice that $2+1+ \frac{1}{2}+ \frac{1}{4}+...+ \frac{1}{64}$ is $S-\frac1{128}$ so:
$$2S-4=S-\frac1{128} \rightarrow S=4-\frac1{128}=\frac{511}{128}$$
