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The sequence {n^√9999} converges to A.0 B.1 C.9999 D.99?
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The sequence {n^√9999} converges to A.0 B.1 C.9999 D.99?
Convergence of the Sequence {n^√9999}
The sequence {n^√9999} can be analyzed to determine its convergence to a specific value.
Understanding the Sequence
The sequence {n^√9999} consists of terms where each term is obtained by raising the index n to the power of the square root of 9999.
Convergence Criteria
To determine the convergence of the sequence, we need to check if the terms in the sequence approach a specific value as n tends to infinity.
Limit Calculation
As n approaches infinity, the square root of 9999 remains constant. Therefore, the sequence converges to a value equal to the square root of 9999 raised to any power, which results in either 0 or 1 depending on the power.
Final Answer
Therefore, the sequence {n^√9999} converges to 1 as n tends to infinity. Hence, the correct answer is B. 1.
The sequence {n^√9999} can be analyzed to determine its convergence to a specific value.
Understanding the Sequence
The sequence {n^√9999} consists of terms where each term is obtained by raising the index n to the power of the square root of 9999.
Convergence Criteria
To determine the convergence of the sequence, we need to check if the terms in the sequence approach a specific value as n tends to infinity.
Limit Calculation
As n approaches infinity, the square root of 9999 remains constant. Therefore, the sequence converges to a value equal to the square root of 9999 raised to any power, which results in either 0 or 1 depending on the power.
Final Answer
Therefore, the sequence {n^√9999} converges to 1 as n tends to infinity. Hence, the correct answer is B. 1.
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The sequence {n^√9999} converges to A.0 B.1 C.9999 D.99?
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The sequence {n^√9999} converges to A.0 B.1 C.9999 D.99? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sequence {n^√9999} converges to A.0 B.1 C.9999 D.99? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sequence {n^√9999} converges to A.0 B.1 C.9999 D.99?.
The sequence {n^√9999} converges to A.0 B.1 C.9999 D.99? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sequence {n^√9999} converges to A.0 B.1 C.9999 D.99? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sequence {n^√9999} converges to A.0 B.1 C.9999 D.99?.
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