Limit Superior — Topic Summaries
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Real Analysis 12 | Examples for Limit Superior and Limit Inferior [dark version]
Limit superior (lim sup) and limit inferior (lim inf) always exist for any real sequence, taking values in the extended real line (real numbers or...
Real Analysis 11 | Limit Superior and Limit Inferior [dark version]
Limit superior and limit inferior turn messy, non-convergent behavior of real sequences into two precise “best possible” accumulation values—largest...
Real Analysis 20 | Ratio and Root Test [dark version]
Ratio and root tests give fast, geometric-series-based ways to decide whether an infinite series a_k converges absolutely. The key payoff is...