Question:
Let \(\left\{a_n\right\}^{\infin}_{n=1}\) be a sequence of real numbers.
Then, which of the following statements is/are always TRUE ?
Let \(\left\{a_n\right\}^{\infin}_{n=1}\) be a sequence of real numbers.
Then, which of the following statements is/are always TRUE ?
Then, which of the following statements is/are always TRUE ?
Updated On: Aug 13, 2024
- If \(\sum\limits_{n=1}^{\infin}a_n\)converges absolutely, then \(\sum\limits_{n=1}^{\infin}a_n^2\) converges absolutely
- If \(\sum\limits_{n=1}^{\infin}a_n\)converges absolutely, then \(\sum\limits_{n=1}^{\infin}a_n^3\) converges absolutely
- If \(\sum\limits_{n=1}^{\infin}a_n\) converges, then \(\sum\limits_{n=1}^{\infin}a^2_n\) converges
- If \(\sum\limits_{n=1}^{\infin}a_n\) converges, then \(\sum\limits_{n=1}^{\infin}a^3_n\) converges
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The Correct Option is A, B
Solution and Explanation
The correct option is (A) : If \(\sum\limits_{n=1}^{\infin}a_n\)converges absolutely, then \(\sum\limits_{n=1}^{\infin}a_n^2\) converges absolutely and (B) : If \(\sum\limits_{n=1}^{\infin}a_n\)converges absolutely, then \(\sum\limits_{n=1}^{\infin}a_n^3\) converges absolutely
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