Lim, sup, and inf

Calculus Level 4

Let $$x_n$$ be the sequence $2,-2^{1/2},2^{1/3},-2^{1/4},2^{1/5},-2^{1/6},\ldots.$ What are the values of $\inf x_n, \quad \liminf_{n\to\infty} x_n, \quad \lim_{n\to\infty} x_n, \quad \limsup_{n\to\infty} x_n, \quad \sup x_n \; ?$

Notation:

• In the choices, $$\text{DNE}$$ means "does not exist."
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