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what is the sum of 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8 I'm

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what is the sum of 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8 I'm [#permalink] New post 05 Feb 2007, 11:04
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what is the sum of
2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8

I'm really confused about the OA :?:

OA 2^9
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 [#permalink] New post 05 Feb 2007, 12:50
Quote:
what is the sum of
2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8
2 + 2 = 4
2^2 = 4
2^3 = 8
2^4 = 16
32, 64, 128, 256

The above will sum to 512.
512 = 2^9

I had to add these. Who has a faster method?
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 [#permalink] New post 05 Feb 2007, 13:21
Other easy way to do this would be to bring out 2 common and keep on doing that:

2(1+1+2+2^2+2^3+2^4+2^5+2^6+2^7)
2(2+2+2^2+2^3+2^4+2^5+2^6+2^7)
2^2 (1+1+2+2^2+2^3+2^4+2^5+2^6)
2^2(2+2+2^2+2^3+2^4+2^5+2^6)
2^3(1+1+2+2^2+2^3+2^4+2^5)
2^3(2+2+2^2+2^3+2^4+2^5)

If you continue to solve this the answer will be:
2^9
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 [#permalink] New post 05 Feb 2007, 13:28
ok... now my answer is really nerd...

use binary numbers:

2 = 000000000001
2^2=4 = 000000000010
2^3=8 = 000000000100
...

2^8 = 256 = 000010000000
------------------------------------
sum = = 000011111111

IF you now add an extra 2 what you get is:

sum = 000011111111
+2 = 000000000001
----------------------------------
total = 000100000000
=2^9
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 [#permalink] New post 05 Feb 2007, 17:11
this is the best way to do this.quickly after 2^3..i realized a pattern it was pretty much easy to see that the answer would 2^9

amorpheus wrote:
Other easy way to do this would be to bring out 2 common and keep on doing that:

2(1+1+2+2^2+2^3+2^4+2^5+2^6+2^7)
2(2+2+2^2+2^3+2^4+2^5+2^6+2^7)
2^2 (1+1+2+2^2+2^3+2^4+2^5+2^6)
2^2(2+2+2^2+2^3+2^4+2^5+2^6)
2^3(1+1+2+2^2+2^3+2^4+2^5)
2^3(2+2+2^2+2^3+2^4+2^5)

If you continue to solve this the answer will be:
2^9
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 [#permalink] New post 06 Feb 2007, 22:51
Sum of a geometric progression

a + a.r + a.r ^2 + a.r^3 ....a.r^(n-1) = a(r^n - 1) / (r - 1)
first term = a
nth term = a . r ^ (n - 1)

Taking a part of the required expr
2 + 2 ^ 2 + 2 ^ 3.....+ 2 ^ 8
2 + 2 .2 + 2. 2^2 + ..... 2.2 ^(8-1)

Here a = 2, r = 2, n = 8 ===> Above expr sum = 2(2 ^ 8 - 1)/(2 -1)

=2 ^ 9 -2


The required expr = 2+ 2+ 2^2 +....2^8 = 2 + 2^9 -2 = 2^9
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Re: GMAT prep question PS [#permalink] New post 08 Feb 2007, 10:48
sjmalu wrote:
what is the sum of
2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8

I'm really confused about the OA :?:

OA 2^9


Assuming S = 2 + 2 + 2^2 + 2^3 + ... + 2^8
S = 2 + 2 + 2^2 + 2^3 + ... + 2^8
2S = 4 + 2^2 + 2^3 + ... + 2^8 + 2^9

Did you notice the repeating term 2^2 + 2^3 + ... + 2^8?
Get rid of this term by
2S - S = S = (2^9 + 4) - (2 + 2) = 2^9
Re: GMAT prep question PS   [#permalink] 08 Feb 2007, 10:48
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