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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!

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  • $\begingroup$ Here is a tutorial on how to type math. $\endgroup$ – Saad Mar 20 '18 at 8:55
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    $\begingroup$ The same series has been discussed here: math.stackexchange.com/questions/2692776/…. $\endgroup$ – Martin R Mar 20 '18 at 8:59
  • $\begingroup$ Yes indeed just discussed earlier, I thought this was a bit different but it is exactly the same. Read the comments to the answer. $\endgroup$ – user Mar 20 '18 at 9:03
  • $\begingroup$ @MartinR I made some hypothesis to deal with this task, what do you think about it? what strategy could bebused to prove that $\sin (1+k^3)\not \to 0$? $\endgroup$ – user Mar 20 '18 at 9:05
  • $\begingroup$ @gimusi: If I knew the answer then I would write an answer :) $\endgroup$ – Martin R Mar 20 '18 at 9:06

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