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In the sequence of numbers a_1,a_2,a_3
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14 May 2020, 13:52
14 May 2020, 13:52
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Question Stats:
63% (01:38) correct
36% (01:18) wrong based on 190 sessions
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In the sequence of numbers \(a_1,a_2,a_3....,a_n......\)is defined by \(a_n=2^n -\frac{1}{2^{n-21}}\) for each integer \(n \neq 1\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The sum of the first 20 terms of this sequence |
The sum of the first 19 terms of this sequence |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Re: In the sequence of numbers a_1,a_2,a_3
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15 May 2020, 05:59
15 May 2020, 05:59
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Carcass wrote:
In the sequence of numbers \(a_1,a_2,a_3....,a_n......\)is defined by \(a_n=2^n -\frac{1}{2^{n-21}}\) for each integer \(n \neq 1\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The sum of the first 20 terms of this sequence |
The sum of the first 19 terms of this sequence |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
We have:
Quantity A: \(a_1 + a_2 + a_3 + ....+ a_{18}+ a_{19}+ a_{20}\)
Quantity B: \(a_1 + a_2 + a_3 + ....+ a_{18}+ a_{19}\)
Subtract \((a_1 + a_2 + a_3 + ....+ a_{18}+ a_{19})\) from both quantities to get:
Quantity A: \(a_{20}\)
Quantity B: \(0\)
GIVEN: \(a_n=2^n -\frac{1}{2^{n-21}}\)
So, \(a_{20}=2^{20} -\frac{1}{2^{20-21}}=2^{20} -\frac{1}{2^{-1}}=2^{20} - 2^{1} =\) (a very very big number) - 2
We get:
Quantity A: (a very very big number) - 2
Quantity B: 0
Answer: A
Cheers,
Brent
Re: In the sequence of numbers a_1,a_2,a_3
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20 Jun 2020, 22:52
20 Jun 2020, 22:52
Hello,
What do you mean by n # 1. for n=1 dont we have : 2-2^20?
What do you mean by n # 1. for n=1 dont we have : 2-2^20?
