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10 Oct 2005, 12:19
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What is the value of 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + 2^9 ?
(A) 2^9
(B) 2^10
(C) 2^16
(D) 2^35
(E) 2^37
At the time I did this, my brain was fried and I couldn't think of an easy way to solve it but there must be. Can someone tell me how, please?
(A) 2^9
(B) 2^10
(C) 2^16
(D) 2^35
(E) 2^37
At the time I did this, my brain was fried and I couldn't think of an easy way to solve it but there must be. Can someone tell me how, please?
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10 Oct 2005, 12:45
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b) 2^10
2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9
=2^2+2^2+2^3+2^4...+2^9
2^3=(2^2)+(2^2), and 2^4=(2^3+2^3)... similarly 2^8+2^8=2^9
by the above, we know that 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8 = 2^9
2^9+2^9=2(2^9)=2^10
This is the simplest method I could think of
2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9
=2^2+2^2+2^3+2^4...+2^9
2^3=(2^2)+(2^2), and 2^4=(2^3+2^3)... similarly 2^8+2^8=2^9
by the above, we know that 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8 = 2^9
2^9+2^9=2(2^9)=2^10
This is the simplest method I could think of
10 Oct 2005, 12:53
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I get B) 2^10
Applied Geometric Progression formula for sum (Sn = a(1-r^n)/1-r)
2+2^1+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9
= 2+ 2(1-2^9)/(-1) = 2 + 2(-511)/(-1) = 2 + 2(511)
= 2 + 1022 = 1024 or 2^10
Applied Geometric Progression formula for sum (Sn = a(1-r^n)/1-r)
2+2^1+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9
= 2+ 2(1-2^9)/(-1) = 2 + 2(-511)/(-1) = 2 + 2(511)
= 2 + 1022 = 1024 or 2^10
