from a practice test:
2+2+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 got e., but the answer is a. Why?
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scoobydooby
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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+[sum of GP with common ratio 2, n=8; a(r^n-1)/(r-1)]
=2+2(2^8-1)/(2-1)
=2+2(2^8-1)
=2+2^9-2
=2^9
=2+(2+2^2+2^3+2^4+2^5+2^6+2^7+2^8)
=2+[sum of GP with common ratio 2, n=8; a(r^n-1)/(r-1)]
=2+2(2^8-1)/(2-1)
=2+2(2^8-1)
=2+2^9-2
=2^9
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dumb.doofus
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You just have to apply geometric series here..
2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8
= 2 + 2 (1+2+2^2+2^3+2^4+2^5+2^6+2^7)
geometric series = a(r^n - 1)/(r-1)
here a = 1, r = 2, n = 8, applying it above gives us
= 2 + 2(2^8 -1)
= 2^9
2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8
= 2 + 2 (1+2+2^2+2^3+2^4+2^5+2^6+2^7)
geometric series = a(r^n - 1)/(r-1)
here a = 1, r = 2, n = 8, applying it above gives us
= 2 + 2(2^8 -1)
= 2^9
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See the pattern:kevind147 wrote:from a practice test:
2+2+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 got e., but the answer is a. Why?
2+2=4=2^2
2^2+2^2=8=2^3
So continuing this way and inducting on the observed pattern, you will end up with
2^8 +2^8=2^9.
thanks this makes the most sense to me, but why is the series multiplied by 2? Why is it 2(2^8-1) instead of just (2^8-1)?scoobydooby 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+[sum of GP with common ratio 2, n=8; a(r^n-1)/(r-1)]
=2+2(2^8-1)/(2-1)
=2+2(2^8-1)
=2+2^9-2
=2^9
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scoobydooby
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that comes from the formula a(r^n-1)/(r-1)
our series: 2+2^2+2^3+2^4+2^5+2^6+2^7+2^8
a=2, r=2, n=8
putting it all in the formula gives 2(2^8-1)
our series: 2+2^2+2^3+2^4+2^5+2^6+2^7+2^8
a=2, r=2, n=8
putting it all in the formula gives 2(2^8-1)
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dumb.doofus
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Nice approach.. quite simple and fast..dtweah wrote:See the pattern:kevind147 wrote:from a practice test:
2+2+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 got e., but the answer is a. Why?
2+2=4=2^2
2^2+2^2=8=2^3
So continuing this way and inducting on the observed pattern, you will end up with
2^8 +2^8=2^9.
One love, one blood, one life. You got to do what you should.
https://dreambigdreamhigh.blocked/
https://gmattoughies.blocked/
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