Simple but forgot the logic

If you don't know where to start, start where you know and pull out a common factor to get going.

(1) Ans = 2(1 + 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7)
(2) =2(4 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7)
(3) =2(2^2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7)

You can see that the 2 2^2 terms equal 8 which is 2^3, so:

(4) =2(2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7)

Factor again with 2^3:

(5) =2^4 (1 + 1 + 2 + 2^2 + 2^3 + 2^4)

Apply same logic as before in eqn (4) to combine the 1 + 1 + 2 + 2^2 = 2^3:

(6) =2^4 (2^3 + 2^3 + 2^4); factor
(7) =2^7 (1 + 1 + 2)
(8) =2^7 (2^2)
(9) =2^9

Hope this helps, good luck

I hit submit before I meant to finish. The above response is what I'd do rather than freezing up and cursing the GMAT if I couldn't think of anything else to do. Alternatively, you could notice that:

{1} 2^x + 2^x = 2 (2^x) = 2^(x+1)

Here you have

2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8
=2^1 + 2^1 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

using the above remark {1} we can make it

=2^2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

and repeat while collapsing:

=2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

until you get:

=2^8 + 2^8 = 2^9

Hope this helps as well.

Thanks Ryan!! The second explanation gave me a clear shot..