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Sequences: Comparing Limits and Squeeze Theorem

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Explanations 1

Just as we can compare limits and use the squeeze theorem to evaluate limits of functions, we can do the same for sequences.
By Victor Wang

Problems 1

What is the value of lim⁡n→∞∑k=0n(nk)−1\lim_{n\to\infty} \sum_{k=0}^{n} \binom{n}{k}^{-1}limn→∞∑k=0n(kn)−1? Here (nk)\binom{n}{k}(kn) is a binomial coefficient. Source: HMMT…