I don't really understand what pep wrote... Here's an easier way to do this problem instead of memorizing some formula that may or may not apply to another problem you're working on. It may be a fine formula, but my eyes usually glaze over those kinds of things... why? because you don't really get an understanding of how solution works. Because the GMAT can't simply be answered with a series of formulas, it's important to get what's going on here.
2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 =
First of all, you should be able to narrow the choices down to A or B really quickly since addition won't cause exponents to rise that quickly.
The key here is to look for patterns. You'll notice that 2^7 is half of 2^8 and that 2^6 is half of 2^7. You should also notice that 2 is a half of 2^4. Now, looking at the first two terms, (2+2), you'll find that they are equal to the next term, 2^2. Similarly, the sum of 2+2+2^2 = 2^3, because each term is twice the previous term (excluding the extra 2 at the beginning).
This pattern continues so that any given term is equal to the sum of all previous terms. Based on this, we can say that everything before the 2^8, is equal to 2^8. We can therefore simplify this whole equation to:
2^8+2^8 which can be further simplified to:
2^8(1+1) = 2^8 * 2 = 2^9.
