Determine whether the series converges/diverges (difficulties with negative terms)

Asked Mar 20 '18 at 08:52

Active Mar 20 '18 at 08:59

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Determine whether the following series converges/diverges:

$$\sum_{k = 1}^\infty \frac{k\sin(1+k^3)}{k+\ln k}.$$

The problem is with $\sin(1+k^3)$. It is also negative and so I do not know which test to use. I did not find any similar problem anywhere.

Could anyone give me a hint, please? Have a nice day! Thanks!

edited Mar 20 '18 at 08:55

Ѕᴀᴀᴅ

asked Mar 20 '18 at 08:52

Daniel

Here is a tutorial on how to type math. – Ѕᴀᴀᴅ Mar 20 '18 at 08:55
2

The same series has been discussed here: https://math.stackexchange.com/questions/2692776/determining-if-a-series-is-absolutely-convergent-or-conditionally-convergent-wit. – Martin R Mar 20 '18 at 08:59
Yes indeed just discussed earlier, I thought this was a bit different but it is exactly the same. Read the comments to the answer. – user Mar 20 '18 at 09:03
@MartinR I made some hypothesis to deal with this task, what do you think about it? what strategy could bebused to prove that $\sin (1+k^3)\not \to 0$? – user Mar 20 '18 at 09:05
@gimusi: If I knew the answer then I would write an answer :) – Martin R Mar 20 '18 at 09:06
@MartinR Then the answer is: we have no answer! :) – user Mar 20 '18 at 09:07
@MartinR Finally we have an aswer! :) – user Mar 21 '18 at 10:22

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