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The sum of the series Sigma n=1 dask to infinity 1/(n-1)! is A. e B. e-1 C. e+1 D. e-2?
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The sum of the series Sigma n=1 dask to infinity 1/(n-1)! is A. e B. e...
Sum of the Series
The given series is: Σn=1 to infinity 1/(n-1)!
Calculating the Sum
To find the sum of this series, we can rewrite the terms using the definition of factorial.
1/(n-1)! can be written as 1/(n-1)(n-2)(n-3)...(3)(2)(1).
This can be further simplified to 1/n!, which is a common form of the terms in the series for n ≥ 1.
So, the series can be rewritten as Σn=0 to infinity 1/n!.
This is a known series which converges to the value e, where e is the base of the natural logarithm.
Final Answer
Therefore, the sum of the series Σn=1 to infinity 1/(n-1)! is A. e.
So, the correct answer is A. e.
The given series is: Σn=1 to infinity 1/(n-1)!
Calculating the Sum
To find the sum of this series, we can rewrite the terms using the definition of factorial.
1/(n-1)! can be written as 1/(n-1)(n-2)(n-3)...(3)(2)(1).
This can be further simplified to 1/n!, which is a common form of the terms in the series for n ≥ 1.
So, the series can be rewritten as Σn=0 to infinity 1/n!.
This is a known series which converges to the value e, where e is the base of the natural logarithm.
Final Answer
Therefore, the sum of the series Σn=1 to infinity 1/(n-1)! is A. e.
So, the correct answer is A. e.
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The sum of the series Sigma n=1 dask to infinity 1/(n-1)! is A. e B. e-1 C. e+1 D. e-2?
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The sum of the series Sigma n=1 dask to infinity 1/(n-1)! is A. e B. e-1 C. e+1 D. e-2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sum of the series Sigma n=1 dask to infinity 1/(n-1)! is A. e B. e-1 C. e+1 D. e-2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the series Sigma n=1 dask to infinity 1/(n-1)! is A. e B. e-1 C. e+1 D. e-2?.
The sum of the series Sigma n=1 dask to infinity 1/(n-1)! is A. e B. e-1 C. e+1 D. e-2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sum of the series Sigma n=1 dask to infinity 1/(n-1)! is A. e B. e-1 C. e+1 D. e-2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the series Sigma n=1 dask to infinity 1/(n-1)! is A. e B. e-1 C. e+1 D. e-2?.
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