Correct Answer - Option 1 : 0
Concept:
Let, an is the nth term of a sequence then if,
\(\mathop {\lim }\limits_{n \to ∞ } {a_n} = 0\)
then the sequence converges else the sequence diverges
Analysis:
Given:
\(a_n={\left\{ {\frac{{\sin \frac{{nx}}{2}}}{n}} \right\}^\infty }\)
\(\mathop {\lim }\limits_{n \to \infty } \frac{{\sin \frac{{nx }}{2}}}{n} \)
The value of sin (∞) is either +1 or -1 so take it as ‘k’
\(= \frac{k}{\infty }\; = 0\)
