Limit problem

[fallen void]

I have the limit of this

$\lim_{n\to\infty}\frac{1}{n^{2}+3}\sum_{k=1}^{n}\cos(\frac{\pi}{n + k})$

[untold current]

s0lder

[fallen void]

i know the limit of a_n * b_n is 0 if one of them is 0 and the other is bounded

but how do I prove that the sum is bounded?

[fallen void]

<@&286206848099549185>

[fallen void]

<@&286206848099549185>

[glacial idol]

you can say that :
$$-1 \leq \cos(\frac{\pi}{k+n}) \leq 1$$

[untold current]

Ævan