Adding exponents problem from pract. Test

[sev]

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


A )2^9

B) 2^10

C) 2^ 16

D) 2^ 35

E) 2^37

Obviously it's not E, but how do you do this problem? The OA is A which is 2^9

Is there any way to do it without actually calculating all of the values, cuz that just doesnt seem right to me.

[smashingdon]

even if you work it out its simple.
expand just the first few ones

it will become
2 + 2 + 4 + 8 + 16 + 2^5 + 2^6 + 2^7 + 2^8
will become
32 + 2^5 + 2^6 + 2^7 + 2^8
2^5 + 2^5 + 2^6 + 2^7 + 2^8
2^5[1+1+2+4+8]
2^5 * 16
2^5 * 2^4
2^9

[bills_e]

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


A )2^9

B) 2^10

C) 2^ 16

D) 2^ 35

E) 2^37

Obviously it's not E, but how do you do this problem? The OA is A which is 2^9

Is there any way to do it without actually calculating all of the values, cuz that just doesnt seem right to me.

2+2 = 2^2. (Adding the first two terms)
2^2 + 2^2 = 2^3 (Adding the above result to the third term)
2^3 + 2^3 = 2^4 (Adding the above result to the fourth term)

.....

2^8+2^8 = 2^9

Therefore, A.