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Sequences and Series
Mathematics · limit-superior-limit-inferior-bolzano-weierstrass
Problem Suppose { x n } n = 1 ∞ \{x_n\}_{n=1}^\infty { x n } n = 1 ∞ ϵ > 0 \epsilon > 0 ϵ > 0 M M M k ≥ M k \geq M k ≥ M x k − ( lim sup n → ∞ x n ) < ϵ and ( lim inf n → ∞ x n ) − x k < ϵ . x_k - \left(\limsup_{n\to\infty} x_n\right) < \epsilon \quad \text{and} \quad \left(\liminf_{n\to\infty} x_n\right) - x_k < \epsilon. x k − ( n → ∞ lim sup x n ) < ϵ and ( n → ∞ lim inf x n ) − x k < ϵ . Browse the problem library