PG entrance exam IIT JAM 2025 Mock Test Mathematical Science Analysis Sequences & Series (Convergence)
Let \((x_n) \) be a sequence defined as:
\(x_n = \left(1 + \frac{1}{n}\right)^n + (-1)^n \frac{1}{n} \), for \(n \in \mathbb{N} \).
Which of the following statements is true?
1
\( (x_n) \) is a Cauchy sequence and converges to e.
2
\( (x_n) \) is not a Cauchy sequence but is bounded.
3
\( (x_n) \) is a Cauchy sequence and diverges.
4
\( (x_n) \) is not a Cauchy sequence and diverges.