Adding Exponents with the Same Bases

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dnkcdnguy: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Sat Sep 06, 2008 12:27 pm

Adding Exponents with the Same Bases

by dnkcdnguy » Sun Jan 18, 2009 7:22 pm

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

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Source: Beat The GMAT — Problem Solving | Sun Jan 18, 2009 7:22 pm

piyush_nitt: Master | Next Rank: 500 Posts; Posts: 424; Joined: Sun Dec 07, 2008 5:15 pm; Location: Sydney; Thanked: 12 times

Re: Adding Exponents with the Same Bases

by piyush_nitt » Sun Jan 18, 2009 10:34 pm

dnkcdnguy wrote: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