Question

Let $(a_n) = (\frac{n+1}{n})$ and $(b_n) = (-1)^n$ be sequences of real number, then

• A. Both $(a_n)$ and $(b_n)$ are convergent
• B. Both $(a_n)$ and $(b_n)$ are divergent
• C. $(a_n)$ is convergent but $(b_n)$ is not convergent
• D. $(a_n)$ is not convergent but $(b_n)$ is convergent

Hint:

To test sequence convergence quickly in exams:
- If the terms approach a single constant value as \(n \to \infty\), it converges.
- If the terms oscillate between different values or grow to \(\pm\infty\), it diverges.

Answer 1

The Correct Option is C