Let (left{x_{n}ight}_{n=1}^{infty}) be a sequence of real numbers defined by (x_{n}=n 2^{-n}), for all (n in mathbb{N}).
Question:
Let \(\left\{x_{n}ight\}_{n=1}^{\infty}\) be a sequence of real numbers defined by \(x_{n}=n 2^{-n}\), for all \(n \in \mathbb{N}\). Compute
\[\liminf _{n ightarrow \infty} x_{n}\]
and
\[\limsup _{n ightarrow \infty} x_{n} \text {. }\]
Determine if the limit of \(x_{n}\) as \(n ightarrow \infty\) exists.
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We can analyze the limit superior limsup and limit inferior liminf of the sequence xn n 2n to determ...View the full answer
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Sinmon Warui Kamau
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