recitation-4-sol.pdf - Analysis Fall 2017 Recitation 4...

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Analysis Fall 2017 Recitation 4: Limsup - Liminf - Cauchy sequences 10/06/2017 Exercise 2.3.13 Let ( x n ) be a sequence such that lim sup n + x n = + and lim inf n + x n = -∞ . 1) Prove that ( x n ) is not convergent. 2) Prove that neither lim n + x n = + nor lim n + x n = -∞ is true. 3) Find an example of such a sequence.

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