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!!

You have
$$2+\sum_{k=0}^7\frac1{2^k}=2+\frac{1-\frac1{2^8}}{1-\frac12}$$
