Question

Determine whether the series converges or diverges Please, check the image

Answer 1

The series as represented in the task content is divergent and hence; diverges.

What convergence and divergence in series?

It follows from the task content that the series defined by the summation expression as represented above is to be identified as divergent or convergent.

It is noteworthy to know that;

If a sequence converges, it means that the limit of the sequence exists as n → ∞. Also, if the limit of the sequence as n → ∞ does not exist, Then, such series is said to diverges.

Therefore, by evaluation as the limit of the expression k sin²k / 1 + k³ as k → ∞ is; Undefined and hence does not exist.

Read more on convergence and divergence of series;

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