Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Let $\langle x_n \rangle$ be a sequence in $\mathbb{R}$, where $x_n = \sin\left(\frac{1}{n}\right)$, then $\langle x_n \rangle$ is convergent in $\mathbb{R}$. Reason R : $\langle x_n \rangle$ is bounded.
In the light of the above statements, choose the correct answer from the options given below

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is NOT the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Hint:

Remember: Convergent $\implies$ Bounded, but Bounded $\centernot\implies$ Convergent! Counterexample: $x_n = (-1)^n$ is bounded in $[-1, 1]$ but oscillates and diverges.

Answer 1

The Correct Option is B