2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^9 2^10 : Quant Question Archive [LOCKED]
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# 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^9 2^10

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Intern
Joined: 11 Oct 2004
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Location: Georgia
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2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^9 2^10 [#permalink]

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14 Jun 2006, 16:19
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

2^9

2^10

2^16

2^35

Exponents are not my forte. I cannot see the rule suppose to apply.
Thought of trying to factor out a common term but did not help

Got it wrong on the test after reviewing can see there is a pattern.

2 + 2 + 2^2 + 2^3 + â€¦â€¦.+ 2^6

= 2^7

What level of difficulty would you rate this question.

Any suggestions on threads to read regarding Exponents.
Thanks.
VP
Joined: 02 Jun 2006
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14 Jun 2006, 16:24
2^9... don't know about level of difficulty... should rate it somewhere below medium, but I am sure other will correct me just in case...
Manager
Joined: 29 Sep 2005
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14 Jun 2006, 16:44
2^9 as well.

Approach was just looking at terms and finding the pattern i.e. 2*2^3....etc etc.

Difficulty would definitely be between medium and easy. Leaning more towards the easy.
GMAT Club Legend
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14 Jun 2006, 17:04
Here's how i would solve it.

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

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

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

= 2^6 + 2^6 + 2^7 + 2^8

= 2^8 + 2^8

= 2^9

Level of difficulty should be slightly below mid range, i guess....
Director
Joined: 06 May 2006
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14 Jun 2006, 23:53
Mmmm..

2 + (2 + 2^2 + 2^3 + ... + 2^8)
= 2 + (sum of first 8 terms of GP with initial value 2 and common multiplying factor 2)
= 2 + [2 x (2^8 - 1)/(2 - 1)]
= 2 + 2^9 - 2
= 2^9

Definitely easy. Once you spot the GP, that is...
[#permalink] 14 Jun 2006, 23:53
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# 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^9 2^10

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