The problem presents a sequence: $\sin 1, 2 \sin \frac{1}{2}, 3 \sin \frac{1}{3}, 4 \sin \frac{1}{4}, ...$ We need to find the general term of this sequence.

AnalysisSequencesLimitsTrigonometry
2025/5/27

1. Problem Description

The problem presents a sequence: sin1,2sin12,3sin13,4sin14,...\sin 1, 2 \sin \frac{1}{2}, 3 \sin \frac{1}{3}, 4 \sin \frac{1}{4}, ...
We need to find the general term of this sequence.

2. Solution Steps

Let ana_n be the nn-th term of the sequence.
Observing the given sequence, we can deduce the general term as:
an=nsin1na_n = n \sin \frac{1}{n}

3. Final Answer

The general term of the sequence is an=nsin1na_n = n \sin \frac{1}{n}.

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