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
= 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8
and so on so forth...
finally u will get 2^8 + 2^8 = 2^9
IMO A
basically see how I have combined the underlined portions of the equation... and how the sum equals to the next higher power of 2...
I would suggest u revise exponents a bit and then try this problem again..
Exponents
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
-
neerajkumar1_1
- Master | Next Rank: 500 Posts
- Posts: 270
- Joined: Wed Apr 07, 2010 9:00 am
- Thanked: 24 times
- Followed by:2 members
-
gmatmachoman
- Legendary Member
- Posts: 2326
- Joined: Mon Jul 28, 2008 3:54 am
- Thanked: 173 times
- Followed by:2 members
- GMAT Score:710
This is a geometric sequence series:
Sum of the series : 2+ 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8
Sn = A1 ( 1- r^n)/ ( 1-r)
A1 = 2
r = An/ An-1
= 4/2 = 2
Sn = 2 ( 1- 2^ 8)/ ( 1-2)
= 2 ( 2^8-1)
We have excluded the first term 2 for computational purpose
2+ Sn
2 + 2 ( 2^8-1)
2( 1 +2^8 -1)
2^9
Pick A
Sum of the series : 2+ 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8
Sn = A1 ( 1- r^n)/ ( 1-r)
A1 = 2
r = An/ An-1
= 4/2 = 2
Sn = 2 ( 1- 2^ 8)/ ( 1-2)
= 2 ( 2^8-1)
We have excluded the first term 2 for computational purpose
2+ Sn
2 + 2 ( 2^8-1)
2( 1 +2^8 -1)
2^9
Pick A
I see how 2^2 + 2^2 = 2^3 and so forth from a numerical aspect, ie if I calculate it out. But that isn't a rule is it? for instance 3^2 + 3^2 does not equal 3^3.neerajkumar1_1 wrote: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
= 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8
and so on so forth...
finally u will get 2^8 + 2^8 = 2^9
IMO A
basically see how I have combined the underlined portions of the equation... and how the sum equals to the next higher power of 2...
I would suggest u revise exponents a bit and then try this problem again..
-
neerajkumar1_1
- Master | Next Rank: 500 Posts
- Posts: 270
- Joined: Wed Apr 07, 2010 9:00 am
- Thanked: 24 times
- Followed by:2 members
oh no no no... see when i calculate 2^2 + 2^2 = 2(2^2) = 2^3vongdn wrote:I see how 2^2 + 2^2 = 2^3 and so forth from a numerical aspect, ie if I calculate it out. But that isn't a rule is it? for instance 3^2 + 3^2 does not equal 3^3.neerajkumar1_1 wrote: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
= 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8
and so on so forth...
finally u will get 2^8 + 2^8 = 2^9
IMO A
basically see how I have combined the underlined portions of the equation... and how the sum equals to the next higher power of 2...
I would suggest u revise exponents a bit and then try this problem again..
but 3^2 + 3^2 = 2(3^2)... that certainly does not equal to 3^3
but if it was 3^2 + 3^2 + 3^2 = 3.(3^2) = 3^3...
as long as u get the math behind what i have just written... then no problems.. .
that makes perfect sense now.....thank youneerajkumar1_1 wrote:oh no no no... see when i calculate 2^2 + 2^2 = 2(2^2) = 2^3vongdn wrote:I see how 2^2 + 2^2 = 2^3 and so forth from a numerical aspect, ie if I calculate it out. But that isn't a rule is it? for instance 3^2 + 3^2 does not equal 3^3.neerajkumar1_1 wrote: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
= 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8
and so on so forth...
finally u will get 2^8 + 2^8 = 2^9
IMO A
basically see how I have combined the underlined portions of the equation... and how the sum equals to the next higher power of 2...
I would suggest u revise exponents a bit and then try this problem again..
but 3^2 + 3^2 = 2(3^2)... that certainly does not equal to 3^3
but if it was 3^2 + 3^2 + 3^2 = 3.(3^2) = 3^3...
as long as u get the math behind what i have just written... then no problems.. .
