Let \( \lim _{n \rightarrow \infty} n \sin (2 \pi e\lfloor n)=k \pi \), where \( n \in N \). Fin...

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Let \( \lim _{n \rightarrow \infty} n \sin (2 \pi e\lfloor n)=k \pi \), where \( n \in N \). Find \( k \) :
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