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# Adding exponents - Easy but its teasing my brain

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Intern
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Adding exponents - Easy but its teasing my brain [#permalink]  22 Jul 2008, 15:18
Hi everyone-

What is the rule in solving this problem:

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

I believe there is a quick way to do this but I can't figure it out.
Thanks
Director
Joined: 12 Jul 2008
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Re: Adding exponents - Easy but its teasing my brain [#permalink]  22 Jul 2008, 15:29
djdela wrote:
Hi everyone-

What is the rule in solving this problem:

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

I believe there is a quick way to do this but I can't figure it out.
Thanks

Are you sure this question is correct?

2 + 2^2 + 2^3 + ... + 2^8 = 510
2^9 = 512
Manager
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Re: Adding exponents - Easy but its teasing my brain [#permalink]  22 Jul 2008, 17:12
The question as is also looks correct. Take 2+2 as 4 or 2^2. This becomes a geometric series with first term 2^2 and ratio=2
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Re: Adding exponents - Easy but its teasing my brain [#permalink]  22 Jul 2008, 17:18
djdela wrote:
What is the rule in solving this problem:

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

It probably was 2^2+2^2+2^3 + ...

the rule is very simple 2^k+2^k = 2*2^k = 2^(k+1)

2^2+2^2 = 2^3, then 2^3+2^3 = 2^4, ... , 2^8+2^8 = 2^9
Director
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Re: Adding exponents - Easy but its teasing my brain [#permalink]  22 Jul 2008, 17:33
maratikus wrote:
djdela wrote:
What is the rule in solving this problem:

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

It probably was 2^2+2^2+2^3 + ...

the rule is very simple 2^k+2^k = 2*2^k = 2^(k+1)

2^2+2^2 = 2^3, then 2^3+2^3 = 2^4, ... , 2^8+2^8 = 2^9

This makes much more sense.
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Re: Adding exponents - Easy but its teasing my brain [#permalink]  22 Jul 2008, 17:50
Hey..

i guess u r all complicating things here..

its is like
2^(1+1+3+4+5+6+7+8) = 2^35
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Re: Adding exponents - Easy but its teasing my brain [#permalink]  22 Jul 2008, 17:50
take the short form of the series.
=> 2 + 2 + 2^2 + 2^3
=> 2(1 + 1 + 2 + 2^2)
=> 2(2 + 2 + 2^2)
=> 2x2 (1 + 1 + 2)
=> 2x2x2 ( 1+1)
=> 2^3 (2) = 2^4

Through same mechanism given sequence will end in 2^8 (2) = 2^9

Last edited by rishi2377 on 22 Jul 2008, 18:01, edited 1 time in total.
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Re: Adding exponents - Easy but its teasing my brain [#permalink]  22 Jul 2008, 17:54
Re: Adding exponents - Easy but its teasing my brain   [#permalink] 22 Jul 2008, 17:54
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