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S is the sum of the first n negative integer powers of 2; i.e.
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26 Aug 2021, 01:55
26 Aug 2021, 01:55
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56% (00:58) correct
43% (00:39) wrong based on 44 sessions
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S is the sum of the first n negative integer powers of 2; i.e. \(S=2^{-1}+2^{-2}+.....+2^{-n}\)
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
s |
1 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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Re: S is the sum of the first n negative integer powers of 2; i.e.
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26 Aug 2021, 20:14
26 Aug 2021, 20:14
Carcass wrote:
S is the sum of the first n negative integer powers of 2; i.e. \(S=2^{-1}+2^{-2}+.....+2^{-n}\)
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
s |
1 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
The terms \(\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, .........., \frac{1}{2^n}\) and are in Geometric progression with common ratio (r) = \(\frac{1}{2}\)
Sum of n terms in G.P with r < 1 is given by; \(S = \frac{a}{(1 - r)}\)
where, \(a\) is the first term and \(r\) is the ratio between 2 consecutive terms
So, \(S = \frac{0.5}{(1 - 0.5)} = \frac{0.5}{0.5} = 1\)
Hence, option C
Re: S is the sum of the first n negative integer powers of 2; i.e.
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23 Nov 2023, 09:07
23 Nov 2023, 09:07
1
KarunMendiratta wrote:
Carcass wrote:
S is the sum of the first n negative integer powers of 2; i.e. \(S=2^{-1}+2^{-2}+.....+2^{-n}\)
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
s |
1 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
The terms \(\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, .........., \frac{1}{2^n}\) and are in Geometric progression with common ratio (r) = \(\frac{1}{2}\)
Sum of n terms in G.P with r < 1 is given by; \(S = \frac{a}{(1 - r)}\)
where, \(a\) is the first term and \(r\) is the ratio between 2 consecutive terms
So, \(S = \frac{0.5}{(1 - 0.5)} = \frac{0.5}{0.5} = 1\)
Hence, option C
The question mentions n negative integer power of 2, thus we know that there are going to be finite set of elements in the sequence. The formula which you used is to get the sum of infinite elements in Geometric Progression. Thus, C cannot be the answer.
