"How to prove the limit lim n →..." was answered by our community

Scott Martinez

Answered question

2022-06-02

How to prove the limit

lim_{n \to \infty} n \sin \frac{2 π}{n} \cos \frac{1}{n}

doesn't exist?

Answer & Explanation

Dolharf1t1y

Beginner2022-06-03Added 1 answers

The limit does exist, one may just write, as

n \to \infty

,

n \sin \frac{2 π}{n} \cos \frac{1}{n} = (2 π) \times \frac{\sin \frac{2 π}{n}}{\frac{2 π}{n}} \times \cos \frac{1}{n} \to 2 π \times 1 \times 1 = 2 π .

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