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The sum of the series 1 + 2 + 4 + 8 + .. to n term
- a)2n –1
- b)2n – 1
- c)1/2n – 1
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The sum of the series 1 + 2 + 4 + 8 + .. to n terma)2n –1b)2n &n...
Important Notes on GP Sum:The sum of GP (of n terms) is: Sn = a(rn - 1) / (r - 1)
Sn = a(rn - 1) / (r - 1)
Sn = 1 (2n - 1) / (2 - 1)
Sn = 2n - 1
Sn = a(rn - 1) / (r - 1)
Sn = 1 (2n - 1) / (2 - 1)
Sn = 2n - 1
Most Upvoted Answer
The sum of the series 1 + 2 + 4 + 8 + .. to n terma)2n –1b)2n &n...
Sum of Geometric Progression Series
Explanation:
The given series is a geometric progression with first term a = 1 and common ratio r=2.
The formula for the sum of n terms of a geometric progression is given by:
S_n = a(1 - r^n)/(1 - r)
Substituting a=1 and r=2, we get:
S_n = 1(1 - 2^n)/(1 - 2)
S_n = 2^n - 1
Therefore, the sum of the given series to n terms is 2^n - 1.
Option Analysis:
Option A: 2n - 1
This is the correct option as it matches with the formula for the sum of the given series.
Option B: 2n + 1
This option is incorrect as the formula for the sum of the given series does not have a term with a positive constant.
Option C: 1/2n + 1
This option is incorrect as it does not match with the formula for the sum of the given series.
Option D: None of these
This option is incorrect as option A is the correct answer.
Conclusion:
The sum of the given series 1, 2, 4, 8, ... to n terms is 2^n - 1. Therefore, the correct option is A.
Explanation:
The given series is a geometric progression with first term a = 1 and common ratio r=2.
The formula for the sum of n terms of a geometric progression is given by:
S_n = a(1 - r^n)/(1 - r)
Substituting a=1 and r=2, we get:
S_n = 1(1 - 2^n)/(1 - 2)
S_n = 2^n - 1
Therefore, the sum of the given series to n terms is 2^n - 1.
Option Analysis:
Option A: 2n - 1
This is the correct option as it matches with the formula for the sum of the given series.
Option B: 2n + 1
This option is incorrect as the formula for the sum of the given series does not have a term with a positive constant.
Option C: 1/2n + 1
This option is incorrect as it does not match with the formula for the sum of the given series.
Option D: None of these
This option is incorrect as option A is the correct answer.
Conclusion:
The sum of the given series 1, 2, 4, 8, ... to n terms is 2^n - 1. Therefore, the correct option is A.
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The sum of the series 1 + 2 + 4 + 8 + .. to n terma)2n –1b)2n – 1c)1/2n – 1d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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