If the nth term of the sequence < an > is given by1n + 12n + 13n + · · + 1n2Verify if < an > is convergent. Also find the limit of sequence.

Question

If the nth term of the sequence < an > is given by1n + 12n + 13n + · · + 1n2Verify if < an > is convergent. Also find the limit of sequence.
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Solution 1

To verify if the sequence is convergent, we need to find the limit as n approaches infinity.

The nth term of the sequence is given by 1/n + 1/2n + 1/3n + ... + 1/n^2.

This is a harmonic series of the form 1/n, which is known to be divergent. However, in this case, each term is divided by an Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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