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GMAT_700
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2 + 2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + 20 Sep 2007, 15:43
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2 + 2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8) = ?

The correct answer should be 2^9



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b14kumar
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2 + 2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + 20 Sep 2007, 15:57
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GMAT_700
2 + 2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8) = ?

The correct answer should be 2^9
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You have to make this series in Geometric Progression and then apply the formula for the "Sum of the n terms of G.P".

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

= 2 + 1 + 1 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8)

= (2+1) + [ 1 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8) ]

Bold portion is G.P

Where a = 1 and r = 2 and n = 9

Sum of the n terms of G.P = a ( (r^n) -1)/(r-1) when r>1

= 1 * ( 2^9 - 1) / (2-1)
= 2^9 -1

Now

(2+1) + [ 1 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8) ]

= (2 + 1 ) + (2^9) -1
= 2 + 2^9

- Brajesh
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beckee529
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2 + 2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + 20 Sep 2007, 17:30
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b14kumar
GMAT_700
2 + 2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8) = ?

The correct answer should be 2^9

You have to make this series in Geometric Progression and then apply the formula for the "Sum of the n terms of G.P".

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

= 2 + 1 + 1 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8)

= (2+1) + [ 1 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8) ]

Bold portion is G.P

Where a = 1 and r = 2 and n = 9

Sum of the n terms of G.P = a ( (r^n) -1)/(r-1) when r>1

= 1 * ( 2^9 - 1) / (2-1)
= 2^9 -1

Now

(2+1) + [ 1 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8) ]

= (2 + 1 ) + (2^9) -1
= 2 + 2^9

- Brajesh
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nice solution.. we dont see a lot of G.P. problems on the forum
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KillerSquirrel
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2 + 2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + 20 Sep 2007, 17:44
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2+2+2+(2^2)+(2^3)+(2^4)+(2^5)+(2^6)+(2^7)+(2^8) = ?

No G.P is needed !!!

since 2+2 = 2^2 and 2^2+2^2 = 2^3 and so on... then:

2+2+2+(2^2)+(2^3)+(2^4)+(2^5)+(2^6)+(2^7)+(2^8) = ?

(2^2)+2+(2^2)+(2^3)+(2^4)+(2^5)+(2^6)+(2^7)+(2^8) = ?

2+(2^3)+(2^3)+(2^4)+(2^5)+(2^6)+(2^7)+(2^8) = ?

2^3+2^3 = 2^4 and so on...

2+(2^8)+(2^8) = ?

2+2^9 = ?

the answer is 2+2^9

:?
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GMATBLACKBELT
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2 + 2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + 20 Sep 2007, 21:18
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GMAT_700
2 + 2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8) = ?

The correct answer should be 2^9
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Im guessin u didn't mean to put an extra 2 at the begining.

All you have to realize is that 2+2 = 2*2 =2^2.

2^2+2^2--> 2(2^2) --- 2^1+2^2 ---> 2^1+2---> 2^3. Just keep doin the same thing.


Ans is 2^9 or 2+2^9 if the 2 was intentional.
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after15
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2 + 2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + 21 Sep 2007, 01:12
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2+2^2 +2^3 +2^4+...2^8 = 2[(2^8 -1)/(2-1)]. In general, a+a^2+...+a^n = a[(a^n -1)/(a-1)]



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