Sequences & limits, rigorously

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Let $a_{n} = \gamma + \alpha\,(-1)^{n} + \dfrac{\beta}{n}$ with $\gamma = 2$, $\alpha = 2$ and $\beta = 2$. Compute $\limsup_{n \to \infty} a_{n}$.

2. Warm-up

   Let $a_{n} = \gamma + \alpha\,(-1)^{n} + \dfrac{\beta}{n}$ with $\gamma = 6$, $\alpha = 5$ and $\beta = 4$. Compute $\limsup_{n \to \infty} a_{n}$.

3. Warm-up

   Let $a_{n} = \gamma + \alpha\,(-1)^{n} + \dfrac{\beta}{n}$ with $\gamma = 4$, $\alpha = 1$ and $\beta = 1$. Compute $\limsup_{n \to \infty} a_{n}$.

Problems shown under their original terms: Generated (template, solver-computed).