Adding Exponents with the Same Bases

[dnkcdnguy]

Can someone show me the best way to solve the following question:

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


Answer: A

Thanks

[piyush_nitt]

Can someone show me the best way to solve the following question:

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


Answer: A

Thanks

2+2[1+2+2^2+2^3+2^4+2^5+2^6+2^7]

figure in bracket is a GP series , a =1 , r = 2 , n = 7

sum of series , a(r^n+1-1)/r-1

2+2[1(2^8-1)/2-1]

2+2(2^8-1)

2+2^9-2

2^9

[dnkcdnguy]

That makes complete sense and I understand it now.

Thanks for your response.