Lebl-Basic-Analysis-I · Problem 2.3.5

Sequences and Series

Mathematics · limit-superior-limit-inferior-bolzano-weierstrass

Problem

a) Let xn:=(−1)nnx_n := \dfrac{(-1)^n}{n}. Find lim sup⁡n→∞xn\displaystyle\limsup_{n\to\infty} x_n and lim inf⁡n→∞xn\displaystyle\liminf_{n\to\infty} x_n. b) Let xn:=(n−1)(−1)nnx_n := \dfrac{(n-1)(-1)^n}{n}. Find lim sup⁡n→∞xn\displaystyle\limsup_{n\to\infty} x_n and lim inf⁡n→∞xn\displaystyle\liminf_{n\to\infty} x_n.

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